Homework For Statistiecs For Psych Sci

PSYS 054 HW#3 – Page 1 of 2

Homework Assignment #3 (10 points) Correlation and Regression

IMPORTANT: Please hand in to the PSYS 054 dropbox by 3pm on Monday, April 1

Part I Imagine that you are a college admissions officer charged with assessing whether SAT scores are predictive of first-year undergraduate grades. You have obtained a small sample of first year students at your institution and have access to their SAT-Verbal score as well as their GPA. The data are presented below (with SAT scores divided by 10 to make the calculation numbers involved a bit smaller). Denote the SAT/10 scores as X and the GPA scores as Y. Round all steps of all answers to 2 decimal places.

Participant SAT/10 First Year GPA A 60 3.9 B 54 3.5 C 48 2.8 D 65 3.8 E 42 2.9 F 58 3.2 G 73 3.5 H 69 3.0 I 55 3.0 J 56 3.4

Assignment: 1. Calculate the correlation coefficient between the two variables in question, showing all work (3 points). 2. Using your textbook, determine whether the correlation is statistically significant and write your result in proper notation (1 point). 3. Calculate the regression equation (based on these data) that one would use to predict GPA from SAT-Verbal scores, showing all work. Based on your model, what would be the predicted GPA for someone scoring an 800 on the SAT-Verbal (and thus with an X score of 80) (3 points)? 4. Create a scatterplot of the observed scores using the blank graph on the next page. Draw the regression line based on your calculations from #3 (1 point). 5. Calculate the standard error of the estimate for the regression line from #4, showing all work (2 points).

PSYS 054 HW#3 – Page 2 of 2

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