The document discusses questions of relationship, which focus on how variables co-vary or correlate with each other. It provides an equation to show that an increase or decrease in variable 1 is accompanied by an increase or decrease in variable 2. As an example, researchers hypothesize that as temperature increases, burglaries increase. Monthly temperature and burglary data is presented and ranked to illustrate that the relative ranks of the two variables are the same, showing a direct relationship between temperature and burglaries.
Multiple regression can be used to explore the relationship between a continuous dependent variable and multiple independent variables. There are three main types of multiple regression: standard, hierarchical, and stepwise. Standard multiple regression involves entering all independent variables into the equation at once to determine how much variance in the dependent variable is explained collectively. The document then provides an example using standard multiple regression to predict perceived stress from measures of control (mastery and PCOISS), finding the model significantly predicts stress and that mastery and PCOISS each uniquely contribute to the prediction.
This study evaluated variables that could predict music achievement in elementary school students. The variables examined were academic achievement, attitude toward music, self-concept in music, music background, and gender. The researcher administered tests to measure these variables and a music achievement test to students in two elementary schools. A multiple regression analysis found that academic achievement, as measured by a standardized test, was the strongest predictor of music achievement scores for both schools. It explained 25% of the variance in one school and 40% of the variance in the other school.
Multiple regression allows examination of the linear relationship between one dependent variable (sales of bar) and two or more independent variables (price of bar and promotion expenditure). The multiple regression equation fits a plane to the data points to predict monthly sales based on price and promotion. The results show that price and promotion are significant predictors of sales, with an increase in price predicted to decrease sales and an increase in promotion predicted to increase sales. The model explains 75.8% of the variation in sales.
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
The document discusses independent and dependent variables in statistics. It explains that the independent variable is the cause or influencer in a study, such as amount of study time or amount of sleep, while the dependent variable is the effect or what is being influenced, such as test scores. It provides examples of how to identify the independent and dependent variables in studies and word problems about viral infections, background noise, and more.
Reporting a single linear regression in apaKen Plummer
The document provides a template for reporting the results of a simple linear regression analysis in APA format. It explains that a linear regression was conducted to predict weight based on height. The regression equation was found to be significant, F(1,14)=25.925, p<.000, with an R2 of .649. The predicted weight is equal to -234.681 + 5.434 (height in inches) pounds.
Diff rel gof-fit - jejit - practice (5)Ken Plummer
The document discusses the differences between questions of difference, relationship, and goodness of fit. It provides examples to illustrate each type of question. A question of difference compares two or more groups on some outcome, like comparing younger and older drivers' average driving speeds. A question of relationship examines whether a change in one variable causes a change in another, such as the relationship between age and flexibility. A question of goodness of fit assesses how well a claim matches reality, such as whether a salesman's claim of software effectiveness fits the results of user testing.
Multiple regression can be used to explore the relationship between a continuous dependent variable and multiple independent variables. There are three main types of multiple regression: standard, hierarchical, and stepwise. Standard multiple regression involves entering all independent variables into the equation at once to determine how much variance in the dependent variable is explained collectively. The document then provides an example using standard multiple regression to predict perceived stress from measures of control (mastery and PCOISS), finding the model significantly predicts stress and that mastery and PCOISS each uniquely contribute to the prediction.
This study evaluated variables that could predict music achievement in elementary school students. The variables examined were academic achievement, attitude toward music, self-concept in music, music background, and gender. The researcher administered tests to measure these variables and a music achievement test to students in two elementary schools. A multiple regression analysis found that academic achievement, as measured by a standardized test, was the strongest predictor of music achievement scores for both schools. It explained 25% of the variance in one school and 40% of the variance in the other school.
Multiple regression allows examination of the linear relationship between one dependent variable (sales of bar) and two or more independent variables (price of bar and promotion expenditure). The multiple regression equation fits a plane to the data points to predict monthly sales based on price and promotion. The results show that price and promotion are significant predictors of sales, with an increase in price predicted to decrease sales and an increase in promotion predicted to increase sales. The model explains 75.8% of the variation in sales.
Multiple regression analysis allows researchers to examine the relationship between one dependent or outcome variable and two or more independent or predictor variables. It extends simple linear regression to model more complex relationships. Stepwise regression is a technique that automates the process of building regression models by sequentially adding or removing variables based on statistical criteria. It begins with no variables in the model and adds variables one at a time based on their contribution to the model until none improve it significantly.
The document discusses independent and dependent variables in statistics. It explains that the independent variable is the cause or influencer in a study, such as amount of study time or amount of sleep, while the dependent variable is the effect or what is being influenced, such as test scores. It provides examples of how to identify the independent and dependent variables in studies and word problems about viral infections, background noise, and more.
Reporting a single linear regression in apaKen Plummer
The document provides a template for reporting the results of a simple linear regression analysis in APA format. It explains that a linear regression was conducted to predict weight based on height. The regression equation was found to be significant, F(1,14)=25.925, p<.000, with an R2 of .649. The predicted weight is equal to -234.681 + 5.434 (height in inches) pounds.
Diff rel gof-fit - jejit - practice (5)Ken Plummer
The document discusses the differences between questions of difference, relationship, and goodness of fit. It provides examples to illustrate each type of question. A question of difference compares two or more groups on some outcome, like comparing younger and older drivers' average driving speeds. A question of relationship examines whether a change in one variable causes a change in another, such as the relationship between age and flexibility. A question of goodness of fit assesses how well a claim matches reality, such as whether a salesman's claim of software effectiveness fits the results of user testing.
This document provides examples of questions that ask for the lowest and highest number in a set of data. The questions ask for the difference between the state with the lowest and highest church attendance, the students with the highest and lowest test scores, and the slowest and fastest versions of a vehicle model.
Inferential vs descriptive tutorial of when to use - Copyright UpdatedKen Plummer
The document discusses the differences between descriptive and inferential statistics. Descriptive statistics are used to describe characteristics of a whole population, while inferential statistics are used when the whole population cannot be measured and conclusions are drawn from a sample to generalize to the larger population. Examples are provided to illustrate when each type of statistic would be used. Key differences include descriptive statistics examining entire populations while inferential statistics examine samples that aim to infer conclusions about populations.
Diff rel ind-fit practice - Copyright UpdatedKen Plummer
The document provides explanations and examples for different types of statistical questions:
- Difference questions compare two or more groups on an outcome.
- Relationship questions examine if a change in one variable is associated with a change in another variable.
- Independence questions determine if two variables with multiple levels are independent of each other.
- Goodness of fit questions assess how well a claim matches reality.
Examples are given for each type of question to illustrate key concepts like comparing groups, examining associations between variables, assessing independence, and evaluating how a claim fits observed data.
Normal or skewed distributions (inferential) - Copyright updatedKen Plummer
- The document discusses determining whether distributions are normal or skewed
- A distribution is considered skewed if the skewness value divided by the standard error of skewness is less than -2 or greater than 2
- For the old car data set in the example, the skewness value of -4.26 divided by the standard error is less than -2, so this distribution is negatively skewed
- The new car data set skewness value of -1.69 divided by the standard error is between -2 and 2, so this distribution is normal
Normal or skewed distributions (descriptive both2) - Copyright updatedKen Plummer
The document discusses normal and skewed distributions and how to identify them. It provides examples of measuring forearm circumference of golf players and IQs of cats and dogs. The forearm circumference data is normally distributed while the dog IQ data is left skewed based on the skewness statistics provided. Therefore, at least one of the distributions (dog IQs) is skewed.
Nature of the data practice - Copyright updatedKen Plummer
The document discusses different types of data:
- Scaled data provides exact amounts like 12.5 feet or 140 miles per hour.
- Ordinal or ranked data provides comparative amounts like 1st, 2nd, 3rd place.
- Nominal data names or categorizes values like Republican or Democrat.
- Nominal proportional data are simply percentages like Republican 45% or Democrat 55%.
Nature of the data (spread) - Copyright updatedKen Plummer
The document discusses scaled and ordinal data. Scaled data can be measured in exact amounts like distances and speeds. Ordinal data provides comparative amounts by ranking items, like the top 3 states in terms of well-being. Examples ask the reader to identify if data is scaled or ordinal, like driving speeds which are scaled, or baby weight percentiles which are ordinal as they compare weights.
The document is a series of questions and examples that explain what it means for a question to ask about the "most frequent response". It provides examples of questions asking about the highest/most number of something based on data in tables or lists. It then asks a series of questions to determine if they are asking about the most frequent/common response based on the data given.
Nature of the data (descriptive) - Copyright updatedKen Plummer
The document discusses two types of data: scaled data and ordinal data. Scaled data can be measured in exact amounts with equal intervals between values. Ordinal or ranked data provides comparative amounts but not necessarily equal intervals. Several examples are provided to illustrate the difference, including driving speed, states ranked by well-being, and elephant weights. Practice questions are also included for the reader to determine if data examples provided are scaled or ordinal.
The document discusses whether variables are dichotomous or scaled when calculating correlations. It provides examples of correlations between ACT scores and whether students attended private or public school. One example has ACT scores as a scaled variable and school type as dichotomous. Another has lower and higher ACT scores as dichotomous and school type as dichotomous. It emphasizes determining if variables are both dichotomous, or if one is dichotomous and one is scaled.
The document discusses the correlation between ACT scores and a measure of school belongingness. It determines that one of the variables, which has a sample size less than 30, is skewed and has many ties. As a result, a non-parametric test should be used to analyze the relationship between the two variables.
The document discusses using parametric versus non-parametric tests based on sample size for skewed distributions. For skewed distributions with a sample size less than 30, a non-parametric test is recommended. For skewed distributions with a sample size greater than or equal to 30, a parametric test is recommended. It provides examples analyzing the correlation between ACT scores and sense of school belongingness using both approaches.
The document discusses whether there are many ties or few/no ties within the variables of the relationship question "What is the correlation between ACT rankings (ordinal) and sense of school belongingness (scaled 1-10)?". It determines that ACT rankings, being ordinal, have many ties, while sense of school belongingness, being on a scale of 1-10, may have many or few ties depending on how scores are distributed.
The document discusses identifying whether variables in statistical analyses are ordinal or nominal. It provides examples of relationships between variables such as ACT rankings and sense of school belongingness, daily social media use and sense of well-being, and private/public school enrollment and sense of well-being. It asks the reader to identify if variables in examples like running speed and shoe/foot size or LSAT scores and test anxiety are ordinal or nominal.
The document discusses covariates and their impact on relationships between variables. It defines a covariate as a variable that is controlled for or eliminated from a study. It explains that if a covariate is related to one of the variables in the relationship being examined, it can impact the strength of that relationship. Examples are provided to demonstrate when a question involves a covariate or not.
This document discusses the nature of variables in relationship questions. It can be determined that the variables are either both scaled, at least one is ordinal, or at least one is nominal. Examples of different relationship questions are provided that fall into each of these categories. The document also provides practice questions for the user to determine which category the variables fall into.
The document discusses the number of variables involved in research questions. It explains that many relationship questions deal with two variables, such as gender predicting driving speed. However, some questions deal with three or more variables, for example gender and age predicting driving speed. The document asks the reader to identify whether example research questions involve two or three or more variables.
The document discusses independent and dependent variables in research questions. It provides examples to illustrate that an independent variable has at least two levels and may have more, such as religious affiliation having two levels (Western religion and Eastern religion) or company type having three levels (Company X, Company Y, Company Z). It then provides a practice example about employee satisfaction rates among morning, afternoon, and evening shifts, identifying shift status as the independent variable with three levels.
The document discusses independent variables and how they relate to research questions. It provides examples of questions with one independent variable, two independent variables, and zero independent variables. An independent variable influences or impacts a dependent variable. Questions are presented about employee satisfaction rates, agent commissions, training proficiency, and cyberbullying incidents to illustrate different numbers of independent variables.
This document discusses dependent and explanatory variables in research questions. It provides examples of questions with one and two dependent variables. A dependent variable is the thing being influenced or measured in a research study. An explanatory variable is what does the influencing. Good research questions will have one or more clearly defined dependent variables and one or more explanatory variables. The document uses examples like shifts' influence on employee satisfaction and training methods' influence on proficiency to illustrate dependent and explanatory variables.
This document provides examples of questions that ask for the lowest and highest number in a set of data. The questions ask for the difference between the state with the lowest and highest church attendance, the students with the highest and lowest test scores, and the slowest and fastest versions of a vehicle model.
Inferential vs descriptive tutorial of when to use - Copyright UpdatedKen Plummer
The document discusses the differences between descriptive and inferential statistics. Descriptive statistics are used to describe characteristics of a whole population, while inferential statistics are used when the whole population cannot be measured and conclusions are drawn from a sample to generalize to the larger population. Examples are provided to illustrate when each type of statistic would be used. Key differences include descriptive statistics examining entire populations while inferential statistics examine samples that aim to infer conclusions about populations.
Diff rel ind-fit practice - Copyright UpdatedKen Plummer
The document provides explanations and examples for different types of statistical questions:
- Difference questions compare two or more groups on an outcome.
- Relationship questions examine if a change in one variable is associated with a change in another variable.
- Independence questions determine if two variables with multiple levels are independent of each other.
- Goodness of fit questions assess how well a claim matches reality.
Examples are given for each type of question to illustrate key concepts like comparing groups, examining associations between variables, assessing independence, and evaluating how a claim fits observed data.
Normal or skewed distributions (inferential) - Copyright updatedKen Plummer
- The document discusses determining whether distributions are normal or skewed
- A distribution is considered skewed if the skewness value divided by the standard error of skewness is less than -2 or greater than 2
- For the old car data set in the example, the skewness value of -4.26 divided by the standard error is less than -2, so this distribution is negatively skewed
- The new car data set skewness value of -1.69 divided by the standard error is between -2 and 2, so this distribution is normal
Normal or skewed distributions (descriptive both2) - Copyright updatedKen Plummer
The document discusses normal and skewed distributions and how to identify them. It provides examples of measuring forearm circumference of golf players and IQs of cats and dogs. The forearm circumference data is normally distributed while the dog IQ data is left skewed based on the skewness statistics provided. Therefore, at least one of the distributions (dog IQs) is skewed.
Nature of the data practice - Copyright updatedKen Plummer
The document discusses different types of data:
- Scaled data provides exact amounts like 12.5 feet or 140 miles per hour.
- Ordinal or ranked data provides comparative amounts like 1st, 2nd, 3rd place.
- Nominal data names or categorizes values like Republican or Democrat.
- Nominal proportional data are simply percentages like Republican 45% or Democrat 55%.
Nature of the data (spread) - Copyright updatedKen Plummer
The document discusses scaled and ordinal data. Scaled data can be measured in exact amounts like distances and speeds. Ordinal data provides comparative amounts by ranking items, like the top 3 states in terms of well-being. Examples ask the reader to identify if data is scaled or ordinal, like driving speeds which are scaled, or baby weight percentiles which are ordinal as they compare weights.
The document is a series of questions and examples that explain what it means for a question to ask about the "most frequent response". It provides examples of questions asking about the highest/most number of something based on data in tables or lists. It then asks a series of questions to determine if they are asking about the most frequent/common response based on the data given.
Nature of the data (descriptive) - Copyright updatedKen Plummer
The document discusses two types of data: scaled data and ordinal data. Scaled data can be measured in exact amounts with equal intervals between values. Ordinal or ranked data provides comparative amounts but not necessarily equal intervals. Several examples are provided to illustrate the difference, including driving speed, states ranked by well-being, and elephant weights. Practice questions are also included for the reader to determine if data examples provided are scaled or ordinal.
The document discusses whether variables are dichotomous or scaled when calculating correlations. It provides examples of correlations between ACT scores and whether students attended private or public school. One example has ACT scores as a scaled variable and school type as dichotomous. Another has lower and higher ACT scores as dichotomous and school type as dichotomous. It emphasizes determining if variables are both dichotomous, or if one is dichotomous and one is scaled.
The document discusses the correlation between ACT scores and a measure of school belongingness. It determines that one of the variables, which has a sample size less than 30, is skewed and has many ties. As a result, a non-parametric test should be used to analyze the relationship between the two variables.
The document discusses using parametric versus non-parametric tests based on sample size for skewed distributions. For skewed distributions with a sample size less than 30, a non-parametric test is recommended. For skewed distributions with a sample size greater than or equal to 30, a parametric test is recommended. It provides examples analyzing the correlation between ACT scores and sense of school belongingness using both approaches.
The document discusses whether there are many ties or few/no ties within the variables of the relationship question "What is the correlation between ACT rankings (ordinal) and sense of school belongingness (scaled 1-10)?". It determines that ACT rankings, being ordinal, have many ties, while sense of school belongingness, being on a scale of 1-10, may have many or few ties depending on how scores are distributed.
The document discusses identifying whether variables in statistical analyses are ordinal or nominal. It provides examples of relationships between variables such as ACT rankings and sense of school belongingness, daily social media use and sense of well-being, and private/public school enrollment and sense of well-being. It asks the reader to identify if variables in examples like running speed and shoe/foot size or LSAT scores and test anxiety are ordinal or nominal.
The document discusses covariates and their impact on relationships between variables. It defines a covariate as a variable that is controlled for or eliminated from a study. It explains that if a covariate is related to one of the variables in the relationship being examined, it can impact the strength of that relationship. Examples are provided to demonstrate when a question involves a covariate or not.
This document discusses the nature of variables in relationship questions. It can be determined that the variables are either both scaled, at least one is ordinal, or at least one is nominal. Examples of different relationship questions are provided that fall into each of these categories. The document also provides practice questions for the user to determine which category the variables fall into.
The document discusses the number of variables involved in research questions. It explains that many relationship questions deal with two variables, such as gender predicting driving speed. However, some questions deal with three or more variables, for example gender and age predicting driving speed. The document asks the reader to identify whether example research questions involve two or three or more variables.
The document discusses independent and dependent variables in research questions. It provides examples to illustrate that an independent variable has at least two levels and may have more, such as religious affiliation having two levels (Western religion and Eastern religion) or company type having three levels (Company X, Company Y, Company Z). It then provides a practice example about employee satisfaction rates among morning, afternoon, and evening shifts, identifying shift status as the independent variable with three levels.
The document discusses independent variables and how they relate to research questions. It provides examples of questions with one independent variable, two independent variables, and zero independent variables. An independent variable influences or impacts a dependent variable. Questions are presented about employee satisfaction rates, agent commissions, training proficiency, and cyberbullying incidents to illustrate different numbers of independent variables.
This document discusses dependent and explanatory variables in research questions. It provides examples of questions with one and two dependent variables. A dependent variable is the thing being influenced or measured in a research study. An explanatory variable is what does the influencing. Good research questions will have one or more clearly defined dependent variables and one or more explanatory variables. The document uses examples like shifts' influence on employee satisfaction and training methods' influence on proficiency to illustrate dependent and explanatory variables.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
6. Here is an equation to use as a guide
An Increase
or decrease in
7. Here is an equation to use as a guide
Variable 1
An Increase
or decrease in
8. Here is an equation to use as a guide
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
9. Here is an equation to use as a guide
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
10. Variable 1
An Increase
or decrease in
By variable we mean
something that varies or
changes, like temperature,
speed, weight, test scores,
is accompanied
by an increase
or decrease in
Variable 2
etc.
15. Researchers hypothesize that as the
temperature increases burglaries increase.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
16. Researchers hypothesize that as the
temperature increases burglaries increase.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
17. Researchers hypothesize that as the
temperature increases burglaries increase.
Temperature
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
18. Researchers hypothesize that as the
temperature increases burglaries increase.
Temperature
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
19. Researchers hypothesize that as the
temperature increases burglaries increase.
Temperature
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Burglaries
20. Researchers hypothesize that as the
temperature increases burglaries increase. Test
this hypothesis with the data set provided.
Therefore, this is a question of
Temperature
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Burglaries
Relationship
21. Let’s see what the data might look like for
this word problem:
22. Let’s see what the data might look like for
this word problem:
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
23. Let’s see what the data might look like for
this word problem:
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
24. Let’s see what the data might look like for
this word problem:
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
25. Let’s see what the data might look like for
this word problem:
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
26. What do we mean when we say that a
relationship exists between two variables – in
this case – temperature and burglaries?
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
27. What we mean is that the two variables vary
(increase or decrease) in either the same or
opposite directions.
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
28. A simple way to illustrate this idea of covary-ing is
to see the relative rank of the values of one
variable and see if those ranks are similar to the
relative rank of the values of the other variable
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
29. Let’s begin by rank ordering the average
temperature values.
Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o 100
30. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul 90o This is the 1h0ig0h est value so we’ll give it a #1 Rank
31. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul #1 90o 100
32. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun 80o 80
Jul #1 90o 100
This is the 2nd highest value so we’ll give it a #2 Rank
33. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun #2
80o 80
Jul #1 90o 100
34. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the 3rd highest value so we’ll give it a #3 Rank
35. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
36. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr 60o 40
May 70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the 4th highest value so we’ll give it a #4 Rank
#3
37. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
38. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the 7th highest value so we’ll give it a #7 Rank
39. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
40. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb 40o 25
Mar 20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the 5th highest value so we’ll give it a #5 Rank
#7
41. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
42. Month Average
Temperature
Number of
Burglaries
Jan 30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the 6th highest value so we’ll give it a #6 Rank
43. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
44. Now, let’s do the same for the number of
burglaries:
Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
45. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o 100
This is the highest
value so we’ll give it a
#1 Rank
46. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o #1
100
47. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o 80
Jul #1 90o #1
100
This is the 2nd highest
value so we’ll give it a
#2 Rank
48. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o #2
80
Jul #1 90o #1
100
49. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o #2
80
Jul #1 90o #1
100
This is the 3rd highest
value so we’ll give it a
#3 Rank
50. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
51. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o 40
May #3
70o 60
Jun #2
80o #2
80
Jul #1 90o #1
100
This is the 4th highest
value so we’ll give it a
#4 Rank #3
52. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
53. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o 5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
This is the 7th highest
value so we’ll give it a
#7 Rank
54. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
55. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o 25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
This is the 5th highest
value so we’ll give it a
#5 Rank
56. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
57. Month Average
Temperature
Number of
Burglaries
Jan #6
30o 10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
This is the 6th highest
value so we’ll give it a
#6 Rank
58. Month Average
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
59. Notice that the relative rank order for
temperature and burglaries across each month
Month Average
Temperature
is the SAME.
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
60. The highest rank on one is the highest rank
Month Average
order on the other.
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
61. The highest rank on one is the highest rank
Month Average
order on the other.
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
62. The 2nd highest rank on one is the 2nd highest
rank order on the other.
Month Average
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
63. Month Average
Temperature
Ect. Ect. Ect.
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
64. This is a way of visualizing how an increase in
one is accompanied by an increase in another.
Month Average
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
65. What would an increase in one variable and an
decrease in another variable look like?
66. What would an increase in one variable and an
decrease in another variable look like?
Month Average
Temperature
Number of
Burglaries
Jan #6
30o #6
10
Feb #5
40o #5
25
Mar #7
20o #7
5
Apr #4
60o #4
40
May #3
70o #3
60
Jun #2
80o #2
80
Jul #1 90o #1
100
67. What would an increase in one variable and an
decrease in another variable look like?
#6 #1
#5
#7
#4
#3
#2
#1
#2
#3
#4
#7
#5
#6
Month Average
Temperature
Number of
Burglaries
Jan 30o 100
Feb 40o 80
Mar 20o 60
Apr 60o 40
May 70o 5
Jun 80o 25
Jul 90o 10
68. What would an increase in one variable and an
decrease in another variable look like?
Month Average
Temperature
Number of
Burglaries
Jan #6 30o #1
100
Feb #5
40o #2
80
Mar #7
20o #3
60
Apr #4
60o #4
40
May #3
70o #7
5
Jun #2
80o #5
25
Jul #1 90o #6
10
69. Notice that in this case, as temperature increases
burglaries decrease.
Month Average
Temperature
Number of
Burglaries
Jan #6 30o #1
100
Feb #5
40o #2
80
Mar #7
20o #3
60
Apr #4
60o #4
40
May #3
70o #7
5
Jun #2
80o #5
25
Jul #1 90o #6
10
71. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
72. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
73. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
74. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
75. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Ice cream
sales
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
76. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Ice cream
sales
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
77. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Ice cream
sales
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
78. An ice cream parlor owner wishes to know the
degree to which ice cream sales are related to
average monthly temperature.
Ice cream
sales
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Temperature
79. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
80. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
81. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
82. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
E.g., a jet can fly as slow as 0 mph and as fast as 700
mph. It’s speed can take on any number of values
in between 0 and 700 (e.g., 2.8 mph or 345.6 mph )
83. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
E.g., A person can be as young as
zero or as old as 100+
(e.g., 6.32 years or 98.9 years)
84. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
85. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
E.g., with gender, male can take on a value of 1
and female a value of 2.
86. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
or
87. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
female can take on a value of 1 and
male a value of 2.
88. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
Year in school can take on a value of
1 for freshmen, 2 for sophomore, 3 for junior
and 4 for senior.
89. Some word problems will look for a relationship
between variables that can take on unlimited
values like speed, age, height or weight
with variables that can take on limited values
like gender, year in school or whether a person
has experienced something or not.
Experience can mean I experienced it = 1 or I did
not experience it = 2 (e.g., exposed to gamma
rays or not exposed to gamma rays)
91. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
92. In this case the wording of our relationship
equation will change from
93. In this case the wording of our relationship
equation will change from
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
94. In this case the wording of our relationship
equation will change from
to
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
95. In this case the wording of our relationship
equation will change from
to
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
Variable 1
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
96. In this case the wording of our relationship
equation will change from
to
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Because variables like
Gender can neither
increase nor decrease
Variable 2
Variable 1
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
97. Let’s see how this works in our word problem
about gender and freeway speed.
98. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
99. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
Variable 1
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
100. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
Variable 1
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
101. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
Freeway
Driving
Speed
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
102. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
Freeway
Driving
Speed
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
103. Researchers wish to know if there is a
relationship between the average freeway
driving speed and gender.
Freeway
Driving
Speed
Higher and
lower scores
in
tend to be
related to
certain groups in
Gender
105. Here is what the data set would look like:
Driver
Mary
Bill
Sarah
Mike
Sally
Charles
Fred
106. Here is what the data set would look like:
Driver Average Freeway
Speed (mph)
Mary 66
Bill 73
Sarah 56
Mike 82
Sally 62
Charles 78
Fred 91
107. Here is what the data set would look like:
Driver Average Freeway
Speed (mph)
Gender
1= male
2 = female
Mary 66 2
Bill 73 1
Sarah 56 2
Mike 82 1
Sally 62 2
Charles 78 1
Fred 91 1
108. Driver Average Freeway
Speed (mph)
Gender
1= male
2 = female
Mary 66 2
Bill 73 1
Sarah 56 2
Mike 82 1
Sally 62 2
Charles 78 1
Fred 91 1
So, are higher
speeds associated
with one gender
and are lower
speeds associated
with the other
gender?
109. Driver Average Freeway
Speed (mph)
Gender
1= male
2 = female
Mary 66 2
Bill 73 1
Sarah 56 2
Mike 82 1
Sally 62 2
Charles 78 1
Fred 91 1
It appears that the
number 2s (female)
have lower average
driving speeds than
110. Driver Average Freeway
Speed (mph)
Gender
1= male
2 = female
Mary 66 2
Bill 73 1
Sarah 56 2
Mike 82 1
Sally 62 2
Charles 78 1
Fred 91 1
. . . the number 1s
(male)
111. Driver Average Freeway
Speed (mph)
Gender
1= male
2 = female
Mary 66 2
Bill 73 1
Sarah 56 2
Mike 82 1
Sally 62 2
Charles 78 1
Fred 91 1
Notice that
this could
sound like a
difference
question.
115. Difference question: Are women faster freeway
drivers than men?
Same question expressed as a relationship:
116. Difference question: Are women faster freeway
drivers than men?
Same question expressed as a relationship:
Does a relationship exist between freeway
speed and gender?
117. Difference question: Are women faster freeway
drivers than men?
Same question expressed as a relationship:
Does a relationship exist between freeway
speed and gender?
Depending on how the question is asked it will
either be a difference or a relationship question.
120. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
121. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
122. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
123. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
124. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
125. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
predict Variable 2
126. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
predict Variable 2
127. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
predict
Writing
Course
Grades
128. To what degree do ACT scores predict college
freshmen grades in a introduction to writing
course.
ACT Scores
An Increase
or decrease in
predict
Writing
Course
Grades
Prediction Questions are classified as
Questions of Relationship
130. Relationship questions ask about the degree to
which a change (increase/decrease) in one
variable is accompanied by a change
(increase/decrease) in another variable.
131. Relationship questions ask about the degree to
which a change (increase/decrease) in one
variable is accompanied by a change
(increase/decrease) in another variable.
Variable 1
An Increase
or decrease in
is accompanied
by an increase
or decrease in
Variable 2
132. Relationship questions can be between variables
that take on unlimited values (e.g, age and
weight, or age and weight),
133. Relationship questions can be between variables
that take on unlimited values (e.g, age and
weight, or age and weight),
Or between variables with limited values (e.g.,
gender and year in school)
134. Relationship questions can be between variables
that take on unlimited values (e.g, age and
weight, or age and weight),
Or between variables with limited values (e.g.,
gender and year in school)
Variable 1
Higher and
lower scores
in
tend to be
related to
certain groups in
Variable 2
136. Finally, relationship questions can focus on the
degree to which one variable predicts another
variable.
Variable 1
An Increase
or decrease in
Predicts Variable 2
137. Some of the words to look for in your problem to
determine if it is a question of relationship are:
138. Some of the words to look for in your problem to
determine if it is a question of relationship are:
• Increase
• Decrease
• Association
• Are associated with
• Relationship
• Relate to
• Predict
• Predictive Power
139. Some of the words to look for in your problem to
determine if it is a question of relationship are:
• Increase
• Decrease
• Association
• Are associated with
• Relationship
• Relate to
• Predict
• Predictive Power