Unit 2 lesson 2
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This document discusses covariance and the Pearson r correlation coefficient. Covariance measures the relationship between two variables, indicating whether it is positive or negative. Pearson r standardizes the covariance to produce a value between -1 and 1 that represents how well one variable can predict the other. It answers whether a relationship exists, its direction, and strength. A value of 0 means no relationship; higher positive or negative values indicate a stronger linear relationship. Pearson r cannot be compared between studies and the covariance determines its sign.
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This document discusses measuring linear association between variables through scatterplots and correlation. It defines correlation as a measure of the strength and direction of linear association between two quantitative variables. Correlation values range from -1 to 1, with -1 indicating a perfect negative linear relationship and 1 indicating a perfect positive linear relationship. The document cautions that correlation only measures linear association and provides an example where data sets with identical correlations show different relationships.
Properties of correlation coefficient
The document discusses properties of the correlation coefficient. It states that the correlation coefficient ranges from -1 to 1, with -1 indicating perfect negative correlation, 1 indicating perfect positive correlation, and 0 indicating no correlation. It also explains that the correlation coefficient is a measure of the strength and linear relationship between two variables and is symmetric, meaning the correlation between variables x and y is the same as between y and x. Additionally, the document defines probable error of the correlation coefficient as a way to determine the limits within which the population correlation coefficient is expected to fall.
Correlation and regression
Correlation and regression are statistical methods used to measure relationships between variables. Correlation determines how strongly two variables are related, yielding a correlation coefficient between -1 and 1. Positive correlation means variables increase together, while negative correlation means one variable decreases as the other increases. Regression finds the best-fit line for predicting a dependent variable from an independent variable. It determines whether knowing one variable provides information to predict another variable. The line of best fit minimizes the sum of squared errors between the observed data points and the fitted line.
procedure for finding correlation coefficient
The coefficient of correlation is a number between -1 and 1 that indicates the strength and direction of the linear relationship between two variables. A value of 0 means no correlation, 1 means perfect positive correlation, and -1 means perfect negative correlation. The coefficient of correlation is calculated using Karl Pearson's method and is denoted by r. It is a dimensionless number that is unaffected by changes in scale or origin of the variables.
Correlation
Correlation measures the strength and direction of association between two variables. It ranges from -1 to 1, where 0 indicates no association and values closer to 1 or -1 indicate stronger positive or negative associations, respectively. The document provides examples of positive correlation between variables such as height and weight that increase together, and negative correlation where variables such as TV time and grades move in opposite directions. Formulas and different types of correlation including partial and multiple correlation are also defined in the document.
4.7 partial correlation
Partial correlation. It was the introduction of relation with the third variables, called multivariate analysis. To find out the relationship between two variables, we need to control one variable. Either the relation will be the same or decrease or increase. Three cases are illustrated to explain the applicability of partial correlation.
Correlation coefficient
This document discusses correlation and the correlation coefficient. It defines correlation as a measure of the relationship between two variables. It explains that the correlation coefficient indicates the magnitude and direction of the relationship as well as the strength of the relationship and percentage of variance explained. Values of the correlation coefficient are interpreted as showing no relationship, a low relationship, or a strong relationship. Conditions for interpreting the correlation coefficient include data forming a linear pattern and equal variances.
Wm 10 portfolio valuation correlation
Correlation is a statistical technique used to determine the strength and direction of the relationship between two variables. The coefficient of correlation (r) measures the statistical correlation and ranges from +1 to -1, where +1 is a perfect positive correlation, -1 is a perfect negative correlation, and 0 is no correlation. Common guidelines for interpreting the coefficient define strong, moderate, and weak correlations based on the absolute value of r. While correlation can examine relationships between quantifiable data, it does not prove causation between variables due to potential confounding factors.
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Practice post
This document discusses measuring linear association between variables through scatterplots and correlation. It defines correlation as a measure of the strength and direction of linear association between two quantitative variables. Correlation values range from -1 to 1, with -1 indicating a perfect negative linear relationship and 1 indicating a perfect positive linear relationship. The document cautions that correlation only measures linear association and provides an example where data sets with identical correlations show different relationships.
Properties of correlation coefficient
The document discusses properties of the correlation coefficient. It states that the correlation coefficient ranges from -1 to 1, with -1 indicating perfect negative correlation, 1 indicating perfect positive correlation, and 0 indicating no correlation. It also explains that the correlation coefficient is a measure of the strength and linear relationship between two variables and is symmetric, meaning the correlation between variables x and y is the same as between y and x. Additionally, the document defines probable error of the correlation coefficient as a way to determine the limits within which the population correlation coefficient is expected to fall.
Correlation and regression
Correlation and regression are statistical methods used to measure relationships between variables. Correlation determines how strongly two variables are related, yielding a correlation coefficient between -1 and 1. Positive correlation means variables increase together, while negative correlation means one variable decreases as the other increases. Regression finds the best-fit line for predicting a dependent variable from an independent variable. It determines whether knowing one variable provides information to predict another variable. The line of best fit minimizes the sum of squared errors between the observed data points and the fitted line.
procedure for finding correlation coefficient
The coefficient of correlation is a number between -1 and 1 that indicates the strength and direction of the linear relationship between two variables. A value of 0 means no correlation, 1 means perfect positive correlation, and -1 means perfect negative correlation. The coefficient of correlation is calculated using Karl Pearson's method and is denoted by r. It is a dimensionless number that is unaffected by changes in scale or origin of the variables.
Correlation
Correlation measures the strength and direction of association between two variables. It ranges from -1 to 1, where 0 indicates no association and values closer to 1 or -1 indicate stronger positive or negative associations, respectively. The document provides examples of positive correlation between variables such as height and weight that increase together, and negative correlation where variables such as TV time and grades move in opposite directions. Formulas and different types of correlation including partial and multiple correlation are also defined in the document.
4.7 partial correlation
Partial correlation. It was the introduction of relation with the third variables, called multivariate analysis. To find out the relationship between two variables, we need to control one variable. Either the relation will be the same or decrease or increase. Three cases are illustrated to explain the applicability of partial correlation.
Correlation coefficient
This document discusses correlation and the correlation coefficient. It defines correlation as a measure of the relationship between two variables. It explains that the correlation coefficient indicates the magnitude and direction of the relationship as well as the strength of the relationship and percentage of variance explained. Values of the correlation coefficient are interpreted as showing no relationship, a low relationship, or a strong relationship. Conditions for interpreting the correlation coefficient include data forming a linear pattern and equal variances.
Wm 10 portfolio valuation correlation
Correlation is a statistical technique used to determine the strength and direction of the relationship between two variables. The coefficient of correlation (r) measures the statistical correlation and ranges from +1 to -1, where +1 is a perfect positive correlation, -1 is a perfect negative correlation, and 0 is no correlation. Common guidelines for interpreting the coefficient define strong, moderate, and weak correlations based on the absolute value of r. While correlation can examine relationships between quantifiable data, it does not prove causation between variables due to potential confounding factors.
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Question 1
The time required for a citizen to complete the 2000 U.S. Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What proportion of the citizens will require less than one hour?
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If the random variable Z has a standard normal distribution, then P(Z ≤ -1.37) is
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15. In a large introductory sociology course, a professor gives two exams. The professor wants to determine whether the scores students receive on the second exam are correlated with their scores on the first exam. To make the calculations easier, a sample of eight students is selected. Their scores are shown in the accompanying table.
Student Exam 1 Exam 2
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...
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Assessment 2 Context
In many data analyses, it is desirable to compute a coefficient of association. Coefficients of association are quantitative measures of the amount of relationship between two variables. Ultimately, most techniques can be reduced to a coefficient of association and expressed as the amount of relationship between the variables in the analysis. There are many types of coefficients of association. They express the mathematical association in different ways, usually based on assumptions about the data. The most common coefficient of association you will encounter is the Pearson product-moment correlation coefficient (symbolized as the italicized r), and it is the only coefficient of association that can safely be referred to as simply the "correlation coefficient". It is common enough so that if no other information is provided, it is reasonable to assume that is what is meant.
Correlation coefficients are numbers that give information about the strength of relationship between two variables, such as two different test scores from a sample of participants. The coefficient ranges from -1 through +1. Coefficients between 0 and +1 indicate a positive relationship between the two scores, such as high scores on one test tending to come from people with high scores on the second. The other possible relationship, which is every bit as useful, is a negative correlation between -1 and 0. A negative correlation possesses no less predictive power between the two scores. The difference is that high scores on one measure are associated with low scores on the other.
An example of the kinds of measures that might correlate negatively is absences and grades. People with higher absences will be expected to have lower grades. When a correlation is said to be significant, it can be shown that the correlation is significantly different form zero in the population. A correlation of zero means no relationship between variables. A correlation other than zero means the variables are related. As the coefficient gets further from zero (toward +1 or -1), the relationship becomes stronger.Interpreting Correlation: Magnitude and Sign
Interpreting a Pearson's correlation coefficient (rXY) requires an understanding of two concepts:
· Magnitude.
· Sign (+/-).
The magnitude refers to the strength of the linear relationship between Variable X and Variable
The rXY ranges in values from -1.00 to +1.00. To determine magnitude, ignore the sign of the correlation, and the absolute value of rXY indicates the extent to which Variable X and Variable Y are linearly related. For correlations close to 0, there is no linear relationship. As the correlation approaches either -1.00 or +1.00, the magnitude of the correlation increases. Therefore, for example, the magnitude of r = -.65 is greater than the magnitude of r = +.25 (|.65| > |.25|).
In contrast to magnitude, the sign of a non-zero correlation is either negative or positive.
These labels are not interpreted ...
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- 2. Covariance Are The Variables Correlated??? “ The average cross-product of the deviation scores.” Answers 2 Questions: 1. Is there any relationship between X and Y? 2. If there is a relationship, is it positive or negative? Next Slide
- 4. Pearson r “ The average cross-product of the standardized deviation scores.” Answers 3 Questions: 1. Is there any relationship between X and Y? 2. If there is a relationship, is it positive or negative? 3. How well does one line describe the data? Next Slide
- 5. Pearson r “ How well does a single line represent my data?” r = .85 r = -.25 r = 1.0 Next Slide
- 6. Pearson r r = .00 Next Slide X 0 0 1 1 Y 0 1 0 1
- 7. “Guessing” Pearson r Height and weight Moderate Positive SES and Math Achievement High Negative Tobacco use and Life Expectancy High Positive GPA and SAT Near Zero Shoe size and IQ Moderate to High Positive Next Slide Parameters Pearson r
- 9. Square Before You Compare R 2 = .25 R 2 = .36 “ Study 2 explains 11% more variance than Study 1” Next Slide Study 1 Pearson r between GPA and GRE r = .50 Study 2 Pearson r between IQ and GRE r = .60
- 10. A Little Practice r = 1.0 r = .832 Next Slide X 5 6 7 8 9 Y 10 12 14 16 18 X 5 6 7 8 9 Y 10 12 14 16 14
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