William H. Knapp III

You will not be able to submit your work for credit, because you are not logged in. Log in!

This homework was due on Monday, December 17 at 06:00 a.m. Turkish time. Late submissions receive half credit.

By checking the box below, you certify that the answers you will submit here represent your own work.

1. If a regression coefficient between some IV and DV is statistically significant, the correlation between those two variables will be equally significant.
True
False

2. If a regression coefficient between some IV and DV is statistically significant, the partial correlation between those two variables will be equally significant.
True
False

3. If a regression coefficient between some IV and DV is statistically significant, the semi-partial correlation between those two variables will be equally significant.
True
False

4. If a regression coefficient between some IV and DV is statistically significant, no other correlations between other DVs with that IV will be equally significant.
True
False

5. If a regression coefficient between some IV and DV is statistically significant, the coefficient of determination will be equally significant.
True
False

6. This is the fourth 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.)
For the next few questions, we'll be concerned with predicting test 2 scores from the number of times students have submitted homework. What's the upper limit of the 99% confidence interval for the correlation between these two variables?

7. How many degrees of freedom do you have to test whether the correlation between test 2 scores and number of submissions is significant?

8. What's the p-value for the test of whether or not the population correlation between test 2 scores and number of submissions is equal to 0?

9. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions. What is the regression coefficient?

10. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions. What is the p-value for the regression coefficient?

11. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions. What is the coefficient of determination?

12. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions. What is the p-value for the coefficient of determination?
NOTICE: If you did everything right, you'll find that the p-values for the correlation, the regression coefficient, and the coefficient of determination are all identical. This is because all of these quantities depend on the same thing (i.e. the correlation) in simple linear regression (i.e. predicting one DV from one IV). In the following examples, we'll see that this does not hold for multiple regression.
Also notice that the p-value for the intercept of the simple linear regression is different from those mentioned earlier.

13. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions, average homework scores, number of homework assignments completed, and test 1 scores. What is the regression coefficient predicting test 2 scores from number of submissions?

14. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions, average homework scores, number of homework assignments completed, and test 1 scores. What is the p-value for the regression coefficient predicting test 2 scores from number of submissions?
NOTICE: This p-value is different from what we found earlier.

15. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions, average homework scores, number of homework assignments completed, and test 1 scores. What is the coefficient of determination?
NOTICE: This is bigger than what is was before because we're able to account for more variance in when we add additional variables that at least partially vary independently of the other variables.

16. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions, average homework scores, number of homework assignments completed, and test 1 scores. What is the p-value for the coefficient of determination?
NOTICE: All of the p-values you found here are different from what they were in the simple linear regression.

17. Create a line of best fit (i.e. least squares) that predicts test 2 scores from number of submissions, average homework scores, number of homework assignments completed, and test 1 scores. What is p-value for the regression constant?

18. What are the residuals that are mentioned in the output for the summary of the linear regression? (Choose all that apply)
Errors.
How much our estimates predicting the DV from one IV differ from the estimates predicting the DV from the other IVs.
How much our predicted values of the DV differ from the observed values.
The degrees of freedom that are left over for significance testing.

19. Why is an Adjusted R-Squared reported in the output for the summary of the linear regression? (Choose all that apply)
Even when there is no correlation in the population, there will usually be some correlation in any finite sample.
It's the value R-squared would be if the linear model was based on semi-partial coefficients.
R-Squared typically over estimates how much variance in the population DV is explained by the IV.
R-Squared typically under estimates how much variance in the population DV is explained by the IV.

20. In previous homework we've discussed that average homework scores were significantly related to test 2 scores. But in our final analysis today, we saw that the regression coefficient for the average homework scores was not statistically significant (i.e. p-value=0.33713). What is reasonable to conclude based on this conflicting information? (Choose all that apply)
There is a relationship between average homework scores and test 2 scores.
There is a unique relationship between average homework scores and test 2 scores after accounting for the other variables.
There is no relationship between average homework scores and test 2 scores.
There is no unique relationship between average homework scores and test 2 scores after accounting for the other variables.
It is impossible to draw any reasonable conclusions from such conflicting data.