Question

SAT	GPA
1610	2.35
1230	2.02
1520	3.78
1360	1.39
1270	1.14
1760	3.23
1420	2.25
1660	2.71
1330	2.81
1200	0.57
1380	3.6
1660	3.11
1640	2.85
1460	2.98
1730	2.94
1350	2.59
1780	3.51
1330	1.7
1750	2.33
1390	1.77
1580	2.13
1790	3.95
1610	2.57
1140	2.25
1400	3.12
1570	0.56
1060	1.62
1840	2.67
1600	2.19
1330	2.66
1540	1.91
1630	2.91
1200	1.39
1510	1.18
1400	2.89

(b) You would like to see whether there is a correlation between students’ SAT score and their College GPA. Let the SAT score be the explanatory (X) variable, and the GPA be the response (Y) variable. Use the software provided in the online classroom to obtain a full regression output

(c) Identify the intercept and slope, and write the regression equation.

(d) If a student’s SAT score is 1143, what is the student’s predicted College GPA? Show calculations.

(d) Identify the coefficient of determination, and interpret the result.

(e) Calculate or identify the coefficient of correlation, and interpret the result.

(f) Identify the 95% confidence interval for the population slope. What are the values in this confidence interval tell you? Be specific.

(g) Does the population slope differ significantly from 0? To answer this question, state the hypotheses, identify the p-value, and interpret the result. Be very detailed here.

(h) Is the SAT score a good predictor for College GPA? Why or why not? Be specific.

(i) What are the values of the 95% confidence interval for the population correlation coefficient provided by the software? How does this result relate to parts (g) and (h)? Be very specific and detailed.

(j) Identify and interpret the smallest negative residual. Provide the complete list of residuals.

Answer 1