William H. Knapp III

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This homework was due on Friday, December 14 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. What does a correlation tell you?
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

2. What does the coefficient of determination tell you?
HINT: Big R squared.
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

3. What does squaring a correlation coefficient tell you?
HINT: Little r squared.
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

4. What does a semi-partial correlation coefficient tell you?
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

5. What does a semi-partial coefficient of determination tell you?
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

6. What does a partial correlation coefficient tell you?
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

7. What does a partial coefficient of determination tell you?
The magnitude and direction of the linear relationship between two variables.
The magnitude and direction of the linear relationship between two variables that have both been adjusted to account for linear relationships with other explanatory variables.
The magnitude and direction of the linear relationship between two variables, one of which (i.e. the independent variable) has been adjusted to account for linear relationships with other explanatory variables.
The percent of variance of one variable that is explained by a linear relationship with another variable.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
The percent of variance of one variable that is uniquely explained by a linear relationship with another variable.
The percent of variance of one variable that hasn't been explained by linear relationships with other variables that is explained by a linear relationship with another variable.
None of the above.

8. What does a regression constant tell you?
How different the means of the two variables are.
How different the predicted mean of the DV is from the observed mean of the DV when the intercept used in the prediction is 0.
How much one variable changes given one unit of change in another variable.
How much one variable changes given one unit of change in another variable holding everything else constant.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
None of the above.

9. What does a regression coefficient tell you?
How different the means of the two variables are.
How different the predicted mean of the DV is from the observed mean of the DV when the intercept used in the prediction is 0.
How much one variable changes given one unit of change in another variable.
How much one variable changes given one unit of change in another variable holding everything else constant.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
None of the above.

10. What does a partial regression coefficient tell you?
How different the means of the two variables are.
How different the predicted mean of the DV is from the observed mean of the DV when the intercept used in the prediction is 0.
How much one variable changes given one unit of change in another variable.
How much one variable changes given one unit of change in another variable holding everything else constant.
The percent of variance of one variable that is explained by linear relationships with one or more other variables.
None of the above.

11. For the next several of questions, you will need to use the following correlations and standard deviations to compute semi-partial and partial correlation coefficients. You will also compute partial regression coefficients a regression constant, and a coefficient of determination.
Imagine three variables, V1, V2, and V3. V1 is the dependent variable.
The standard deviations are as follows:
v1: 14
v2: 28
v3: 17
The correlations between pairs of variables are as follows:
v1 & v2: .58
v2 & v3: -.29
v1 & v3: -.85
The means of the variables are as follows:
v1: 13
v2: 10
v3: 100
What is the semi-partial correlation coefficient explaining v1 from v2?
HINT: Use the formulas from the slides to compute this and the rest of the questions directly. Save the answers in a variable so you don't make rounding errors later.
WARNING: Make sure you use parentheses to get the right answer for this question and those following.

12. What's the partial coefficent of determination for explaining v1 from v2 controlling for v3?
HINT: I'm asking for a coefficient of determination, not correlation coefficient.

13. What's the partial regression coefficent for explaining v1 from v2 controlling for v3?
HINT: There's a difference between correlation and regression coefficients. The regression coefficient is the slope we'll need.

14. What is the semi-partial correlation coefficient explaining v1 from v3 controlling for v2?

15. What's the partial correlation coefficient for explaining v1 from v3 controlling for v2?
HINT: partial CORRELATION coefficient. NOTE: Your answer should be absolutely bigger than the semi-partial correlation.

16. What's the partial regression coefficent for explaining v1 from v3 controlling for v2?

17. What's the regression constant for predicting v1 from v2 and v3?
HINT: Find the intercept.

18. This is the third homework that you'll use data about the class' performance on homework and exams. The data contain a lot of different variables. I encourage you to use str to take a look at the data. stud contains a number linking students to their various scores. hw1-hw26 contains the scores students got on the homework assignments up to this point. t1 and t2 are the test scores for the first and second exams. hwavg contains the mean score for the 26 assignments. submissions contains the number of times students have submitted homework. Finally, hwcompleted contains the number of homework assignments that students completed (i.e. homework that they submitted regardless of the score they received.)
Before you answer the following questions, I recommend verifying that the partial regression coefficient we found in class is correct since you'll need both regression coefficients to find the regression constant to predict values of test 2 scores. What's the partial regression coefficient for predicting test 2 scores from homework scores while controlling for test 1 scores?

19. What's the regression constant for predicting test 2 scores from homework and test 1 scores?

20. What's the coefficient of determination for predicting test 2 scores from homework scores and homework submissions?