William H. Knapp III

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This homework was due on Wednesday, December 12 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. If you observed a correlation of .53, what percent of variance is not explained by the linear relationship between the variables. HINT: Percents should vary between 0 and 100, not 0 and 1.

2. If the linear relationship between two variables explains 48% of the variance in the dependent variable, what is the absolute value of the correlation.

3. If you took z-scores for two variables and found the correlation between the two transformed variables to be -.61, what would the slope of the line of best fit be for predicting the z-score on the DV from the z-score on the IV?
HINT: You should know the mean, variance, and standard deviations for z-scores.

4. If you took z-scores for two variables and found the correlation between the two transformed variables to be -.61, what would the intercept of the line of best fit be for predicting the z-score on the DV from the z-score on the IV?
HINT: You should know the mean, variance, and standard deviations for z-scores.

5. This is the second 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.)
What's the observed value of t for the correlation between the test 1 and 2 scores?

6. For the null hypothesis that the population correlation is equal to 0 and an alpha of .01 what is the upper critical value of t?

7. What's the probability of observing a correlation as or more extreme than what you observed if the null were true?

8. What percent of the variance of test 2 scores is explained by the linear relationship with test 1 scores?
HINT: Percents should vary between 0 and 100, not 0 and 1.

9. When predicting test 2 scores from test one scores, what is the slope that will give us the best fit?

10. When predicting test 2 scores from test one scores, what is the y-intercept that will give us the best fit?

11. What's the observed value of t for the correlation between test 2 and average homework scores?

12. If the null hypothesis was that the population correlation between average homework and test two scores is less than or equal to 0, what's the probability of observing a correlation as or more extreme as the one observed?

13. What percent of the variance of test 2 scores is explained by the linear relationship with average homework scores?
HINT: Percents should vary between 0 and 100, not 0 and 1.

14. What percent of the variance of average homework scores is explained by the linear relationship with test 2 scores?
HINT: Percents should vary between 0 and 100, not 0 and 1.

15. When predicting test 2 scores from average homework scores, what is the slope that will give us the best fit?

16. When predicting test 2 scores from average homework scores, what is the y-intercept that will give us the best fit?

17. When predicting test 2 scores from average homework sccores, what's the sum of the squared differences between the predicted and real test 2 scores?
HINT: For each average homework score, you'll need to make a prediction based on the slope and intercept you found above.

18. If you were trying to predict average homework scores from test 2 scores, what is the slope that will give us the best fit?

19. If you were trying to predict average homework scores from test 2 scores, what is the y-intercept that will give us the best fit?

20. If I lost someone's average homework score and they got an 85 on test 2, what's my best prediction of their average homework score?