This document provides an overview of simple linear regression and correlation. It discusses key concepts such as dependent and independent variables, scatter diagrams, regression analysis, the least-squares estimating equation, and the coefficients of determination and correlation. Scatter diagrams are used to determine the nature and strength of relationships between variables. Regression analysis finds relationships of association but not necessarily of cause and effect. The least-squares estimating equation models the dependent variable as a function of the independent variable.
This presentation describes the application of regression analysis in research, testing assumptions involved in it and understanding the outputs generated in the analysis.
Regression Analysis presentation by Al Arizmendez and Cathryn LottierAl Arizmendez
We present an overview of regression analysis, theoretical construct, then provide a graphic representation before performing multiple regression analysis step by step using SPSS (audio files accompany the tutorial).
This was a presentation I gave to my firm's internal CPE in December 2012. It related to correlation and simple regression models and how we can utilize these statistics in both income and market approaches.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
in this presentation, I've tried to compile all the details about bivariate linear regression and correlation. This presentation has all the key issues addressed, but those who want to use it have to speak more and verbally describe all the details covered according to the understanding of your audience group. Hope you find it useful
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.In this presentation a brief introduction about SLR and MLR and their codes in R are described
This presentation describes the application of regression analysis in research, testing assumptions involved in it and understanding the outputs generated in the analysis.
Regression Analysis presentation by Al Arizmendez and Cathryn LottierAl Arizmendez
We present an overview of regression analysis, theoretical construct, then provide a graphic representation before performing multiple regression analysis step by step using SPSS (audio files accompany the tutorial).
This was a presentation I gave to my firm's internal CPE in December 2012. It related to correlation and simple regression models and how we can utilize these statistics in both income and market approaches.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
in this presentation, I've tried to compile all the details about bivariate linear regression and correlation. This presentation has all the key issues addressed, but those who want to use it have to speak more and verbally describe all the details covered according to the understanding of your audience group. Hope you find it useful
Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest. Regression analysis is a reliable method of identifying which variables have impact on a topic of interest. The process of performing a regression allows you to confidently determine which factors matter most, which factors can be ignored, and how these factors influence each other.In this presentation a brief introduction about SLR and MLR and their codes in R are described
Join CMT Level 1, 2 & 3 Program Courses & become a professional Technical Analyst, CMT USA Best COACHING CLASSES. CMT Institute Live Classes by Expert Faculty. Exams are available in India. Best Career in Financial Market.
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SS
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Simple RegressionSimple Regression
pter
Chapter ContentsChapter Contents
12
12.1 Visual Displays and Correlation Analysis12.1 Visual Displays and Correlation Analysisp y yp y y
12.2 Simple Regression12.2 Simple Regression
12 3 Regression Terminology12 3 Regression Terminology12.3 Regression Terminology12.3 Regression Terminology
12.4 Ordinary Least Squares Formulas12.4 Ordinary Least Squares Formulas
12 T f Si ifi12 T f Si ifi12.5 Tests for Significance12.5 Tests for Significance
12.6 Analysis of Variance: Overall Fit12.6 Analysis of Variance: Overall Fit
12.7 Confidence and Prediction Intervals for 12.7 Confidence and Prediction Intervals for YY
12-1
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Simple RegressionSimple Regression
pter
Chapter ContentsChapter Contents
12
12 8 Residual Tests12 8 Residual Tests12.8 Residual Tests12.8 Residual Tests
12.9 Unusual Observations12.9 Unusual Observations
12 10 Oth R i P bl12 10 Oth R i P bl12.10 Other Regression Problems12.10 Other Regression Problems
12-2
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Simple RegressionSimple Regression
Chapter Learning Objectives (LO’s)Chapter Learning Objectives (LO’s)
12
Chapter Learning Objectives (LO s)Chapter Learning Objectives (LO s)
LO12LO12--1: 1: Calculate and test a correlation Calculate and test a correlation coefficient coefficient for for significancesignificance..
LO12LO12--2: 2: Interpret Interpret the slope and intercept of a regression equation.the slope and intercept of a regression equation.
LO12LO12--3: 3: Make Make a prediction for a given a prediction for a given x value using a x value using a regressionregression
equationequation..qq
LO12LO12--4: 4: Fit a simple regression on an Excel scatter plot.Fit a simple regression on an Excel scatter plot.
LO12LO12--5:5: Calculate and interpretCalculate and interpret confidenceconfidence intervals forintervals for regressionregressionLO12LO12 5: 5: Calculate and interpret Calculate and interpret confidence confidence intervals for intervals for regressionregression
coefficientscoefficients..
LO12LO12 6:6: Test hypotheses about the slope and intercept by usingTest hypotheses about the slope and intercept by using t testst tests
12-3
LO12LO12--6: 6: Test hypotheses about the slope and intercept by using Test hypotheses about the slope and intercept by using t tests.t tests.
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Analysis of VarianceAnalysis of Variance
Ch t L i Obj ti (LO’ )Ch t L i Obj ti (LO’ )
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Chapter Learning Objectives (LO’s)Chapter Learning Objectives (LO’s)
LO12LO12--7:7: Perform regression with Excel or other software.Perform regression with Excel or other software.
LO12LO12--8:8: Interpret the standard errorInterpret the standard error RR22 ANOVA table and F testANOVA table and F testLO12LO12 8: 8: Interpret the standard error, Interpret the standard error, RR , ANOVA table, and F test., ANOVA table, and F test.
LO12LO12--9:9: Distinguish between confidence and prediction intervals.Distinguish between conf.
Factor Analysis and Correspondence Analysis Composite and Indicator Scores of...Matthew Powers
Demonstration of two methods of translating ordinal Likert variables into indicator scores that are appropriate for data visualization and statistical analysis.
7th edition Statistics for Management
Inferential Statistics
International Business School, Hanze university of Applied Science, Groningen, The Netherlands
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
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A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
How libraries can support authors with open access requirements for UKRI fund...
Lesson 4
1. Hanze University of
Applied Science
Groningen
Ning Ding, PhD
Lecturer of International Business
School (IBS)
n.ding@pl.hanze.nl
2. What we are going to learn?
• Review
• Chapter 12: Simple Regression and Correlation
– dependent / independent variables
– scatter diagrams
– regression analysis
– Least-squares estimating equation
– the coefficient of determination
– the coefficient of correlation
3. Review
• Review What is the interquartile range?
a. 98 b. 1764 c. 854 d.484 e.1940 f.2038
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares Interquartile Range
estimating equation 3-Q1
=Q
–the coefficient of =2205-1721
determination =484
–the coefficient of
correlation
4. Review
• Review
• Chapter 12: L=(8+1)*25%=2.25
Simple Regression
and Correlation Range
Interquartile Q1=133.5
–dependent /
=274.5-133.5
independent
=141 L=(8+1)*75%=6.75
variables
–scatter diagrams
–regression analysis
Q3=274.5
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
5. Median Quartile Decile Percentile
1
1 1st D
2
2 Q1=2
2
2
4
4 Interquartile
5 5 Range
7
7
8
8 Q3=8.5
9
9
12
12 9th D
Boxplot
How to interpret?
http://cnx.org/content/m11192/latest/
6. Review
a. Positive b. Negative
c. Symmetrical d. No idea
a b
Mean= € 450
€ 20 € 2000
Q1= € 250 Median= € 350 Q3= € 850
The distribution is skewed to __________ because the mean is
the right
larger than
__________the median.
http://cnx.org/content/m11192/latest/
7. 0.8
1.0
Mean > Median
1.0
1.2
1.2
1.3
1.5
1.7
2.0
2.0
2.1
2.2
2.0
4.0 Mean < Median
3.2
Positively skewed 3.6
3.7
4.0
4.2
4.2
4.5
4.5
4.6
4.8
http://qudata.com/online/statcalc/ 5.0
Negatively skewed
5.0
8. • Review
This means that the data is
• Chapter 12:
symmetrically distributed.
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Zero skewness
mode=median=mean
9. Regression Analysis
• Review
• Chapter 12:
– scatter diagrams
Simple Regression
and Correlation
– dependent / independent variables
–dependent /
independent – regression analysis
variables
–scatter diagrams – Least-squares estimating equation
–regression analysis
–Least-squares – the coefficient of determination
estimating equation
–the coefficient of – the coefficient of correlation
determination
–the coefficient of
correlation
10. Scatter Diagram
• Review –How to determine both the nature and the
• Chapter 12:
strength of a relationship between variables.
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
13. catter DiagramDiagram
Scatter Examples
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
No correlation
14. Scatter Diagram
• Review
Scatter Diagrams:
• Chapter 12: • Patterns indicating that the variables are related
Simple Regression
and Correlation • If related, we can describe the relationship
–dependent /
independent
variables
–scatter diagrams
–regression analysisStrong & Positive Weak & Positive
–Least-squares correlation correlation
estimating equation
–the coefficient of
determination
–the coefficient of No
correlation correlation
Weak & Negative Strong & Negative
correlation correlation
15. Dependent/Independent Variables
Describing Relations
Variables:
Variables – known
• Review
– Independent variables: Scatter D
• Chapter 12:
Simple Regression – Dependent variables: to predict
and Correlation
–dependent /
independent Dependent Variable
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Independent Variable
16. Regression Analysis
Correlation & Cause Effect?
• Review
• The relationships found by regression to be
• Chapter 12: relationships of association
Simple Regression
and Correlation
• Not necessarilly of cause and effect.
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
18. Least-squares Estimating Equation
• Review Least-squares estimating equation:
• Chapter 12:
• The dependent variable Y is determined by the independent
Simple Regression variable X
and Correlation
–dependent /
Dependent Variable
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of Y
correlation
X
I 88 ?
Independent Variable
Ŷ = a + bX
19. Least-squares Estimating Equation
• Review
Least-squares estimating equation:
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
Ŷ = a + bX
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
20. Least-squares Estimating Equation
• Review
Least-squares estimating equation:
• Chapter 12:
Simple Regression
and Correlation
xy - n x y
–dependent /
independent
variables
b= 2 2
–scatter diagrams
–regression analysis
x -nx
–Least-squares
estimating equation
–the coefficient of
determination
Y = a + bX a = Y - bX
–the coefficient of
correlation
21. Least-squares Estimating Equation
the relationship between the age of a truck and the annual repair expense?
• Review xy - nx y
b= Y = a + bX a = Y - bX
x -nx
2 2
Step 2:
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation Step 1: X=3 Y=6
–the coefficient of
determination 78 - 4 * 3 * 6
–the coefficient of
Step 4: b= 0.75 Step 6: Ŷ = 3.75 + 0.75 X
correlation 44 - 4 * 9
a = 6 - 0.75*3 = 3.75 Step 7: 6.75 = 3.75 + 0.75 * 4
Step 5:
If the city has a truck that is 4 years old,
Step 8:
the director could use the equation to predict $675 annually in repairs.
22. Least-squares Estimating Equation
• Review
To find the simple/linear regression of Personal Income (X)
and Auto Sales (Y)
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
If X=64, what about Y?
–Least-squares
estimating equation
–the coefficient of Step 1: Count the number of values. N = 5
determination
a. 4.1 Step 2: Find XY, X2 See the below table
–the coefficient of
b. 5.3
correlation
c. 6.7
d. 7.4
e. 7.5
f. 8.2
23. Least-squares Estimating Equation
• Review
• Chapter 12:
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams Step 3: Find ΣX, ΣY, ΣXY, ΣX2.
–regression analysis ΣX = 311 Mean = 62.2
–Least-squares ΣY = 18.6 Mean = 3.72
estimating equation ΣXY = 1159.7
–the coefficient of
ΣX2 = 19359
determination
–the coefficient of
correlation Step 4: xy - nx y
b=
-nx
2 2
x
Substitute in the above slope formula given.
Slope(b) = 1159.7-5*62.2*3.72 = 0.19
19359-5*62.2*62.2
24. Least-squares Estimating Equation
• Review
Slope(b) = 0.19
• Chapter 12: Now, again substitute in the above intercept formula given.
Step 5:
Simple Regression
and Correlation Intercept(a) = Y - bX = 3.72- 0.19 * 62.2= -8.098
–dependent /
independent Step 6:
variables
Then substitute these values in regression equation
–scatter diagrams formula
–regression analysis Regression Equation(Ŷ) = a + bX
–Least-squares
estimating equation Ŷ = -8.098 + 0.19X
–the coefficient of
determination Regression Equation:
–the coefficient of Suppose if we want to know the
Ŷ = a + bX
correlation approximate y value for the variable X
= -8.098 + 0.19(64)
= -8.098 + 12.16 = 64. Then we can substitute the value
= 4.06
in the above equation.
25. Standard Error
• Review Standard Error:
to minimize the sum of the squares of the errors to measure the
• Chapter 12: goodness of fit of a line
Simple Regression
and Correlation
–dependent /
SE SE
independent ei = residuali
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
Strong Weak
correlation correlation
26. Standard Error
• Review
• Chapter 12: ei = residuali
Simple Regression
and Correlation
–dependent /
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
27. Coefficient of Determination
• Review Correlation Analysis:
• Chapter 12: describe the degree to which one variable is linearly
Simple Regression related to another.
and Correlation
–dependent /
independent
variables Coefficient of Determination: r 2
–scatter diagrams
–regression analysis Measure the extent, or strength, of the association that
–Least-squares
estimating equation
exists between two variables.
–the coefficient of
determination
–the coefficient of
correlation Coefficient of Correlation: r
Square root of coefficient of determination
28. Coefficient of Determination
Coefficient of Determination:
• Review
r2
• Chapter 12: • 0 ≤ r2 ≤ 1.
Simple Regression • The larger r2 , the stronger the linear relationship.
and Correlation
–dependent /
• The closer r2 is to 1, the more confident we are in
independent our prediction.
variables
–scatter diagrams
–regression analysis
–Least-squares
estimating equation
r 2=0.9984
–the coefficient of
determination
–the coefficient of
correlation
29. Coefficient of Determination
• Review
• Chapter 12: • 76.30% of Sales changes is explained by
Simple Regression GDP changes. The rest 23.70% is
and Correlation
–dependent /
explained by other variables.
independent
variables
–scatter diagrams
–regression analysis
–Least-squares
r 2=0.7630
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
30. Coefficient of Correlation
• Coefficient of correlation:
Review
r
• Chapter 12: • r ≤ 0.3 Weak Correlation
Simple Regression
and Correlation
• 0.3 ≤ r ≤ 0.7 Moderate Correlation
–dependent / • r ≥ 0.7 Strong Correlation
independent
variables • r = 0.10 Perfect Correlation r 2=0.1132
–scatter diagrams
–regression analysis
–Least-squares
r =0.1064
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
31. Coefficient of Correlation
• Review • There is a positive and weak correlation
• Chapter 12:
r between GDP and Envy Rides’ annual
Simple Regression sales.
and Correlation • 11.32% of Sales changes is explained by
–dependent /
independent
r 2 GDP changes. The rest 88.68% is
variables r 2=0.1132
–scatter diagrams
explained by other variables.
–regression analysis
–Least-squares
r =0.1064
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
32. Coefficient of Correlation
• Review
• There is a positive and strong correlation
r between GDP and Envy Rides’ annual
• Chapter 12:
Simple Regression
sales.
and Correlation • 76.30% of Sales changes is explained by
–dependent /
r 2 GDP changes. The rest 23.70% is
independent
variables explained by other variables. r 2=0.7630
–scatter diagrams
–regression analysis
–Least-squares r =0.8735
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
33. Coefficient of Correlation
• Review • There is a positive and almost perfect
• Chapter 12: r correlation between GDP and Envy Rides’
Simple Regression annual sales.
and Correlation • 99.84% of Sales changes is explained by
–dependent /
independent r 2 GDP changes. The rest 8% is explained by
variables other variables.
–scatter diagrams r 2=0.9984
–regression analysis
–Least-squares
estimating equation r =0.9992
–the coefficient of
determination
–the coefficient of
correlation
34. Review
• Review
• Chapter 12:
Simple Regression
Which value of r indicates a stronger correlation than 0.40?
and Correlation
–dependent /
A. -0.30
independent B. -0.50
variables C. +0.38
–scatter diagrams D. 0
–regression analysis
–Least-squares
estimating equation If all the plots on a scatter diagram lie on a straight line, what is the
–the coefficient of standard error of estimate?
determination
A. -1
–the coefficient of
correlation B. +1
C. 0
D. Infinity
35. Review
• Review
• Chapter 12:
Simple Regression In the least squares equation, Ŷ = 10 + 20X the value of 20
and Correlation indicates
–dependent / A. the Y intercept.
independent
variables B. for each unit increase in X, Y increases by 20.
–scatter diagrams C. for each unit increase in Y, X increases by 20.
–regression analysis D. none of these.
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
36. Review
• Review
A sales manager for an advertising agency believes there is a
• Chapter 12: relationship between the number of contacts and the amount of the
Simple Regression sales. To verify this belief, the following data was collected:
and Correlation
–dependent / What is the Y-intercept of the linear equation?
independent
A. -12.201
variables
B. 2.1946
–scatter diagrams
C. -2.1946
–regression analysis
D. 12.201
–Least-squares
estimating equation
–the coefficient of
determination
–the coefficient of
correlation
37. What we have learnt?
• Review
• Chapter 12:
– scatter diagrams
Simple Regression
and Correlation
– dependent / independent variables
–dependent /
independent – regression analysis
variables
–scatter diagrams – Least-squares estimating equation
–regression analysis
–Least-squares – the coefficient of determination
estimating equation
–the coefficient of – the coefficient of correlation
determination
–the coefficient of
correlation