Construct a 95% confidence interval for the slope of the regression line in Exercise 1. Interpret the meaning of the interval. Be sure to state it in the context of the data and the question about the data.

Data From Exercise 1

Does attending college pay back the investment? What factors predict higher earnings for graduates? Money magazine surveyed graduates, asking about their point of view of the colleges they had attended (Money’s Best Colleges at new.time.com/money/best-colleges/rankings/best-colleges/). One good predictor of early career earnings ($/year) turned out to be the average SAT score of entering students. Here are the regression model and associated plots. Write the regression model and explain what the slope coefficient means in this context.

Response variable is: Earn R squared = 30.7% s = 5603 with 706 - 2= 704 degrees of freedom Variable Intercept 14468.1 SAT 27.2642 Coefficient SE(Coeff) 1777 1.545 Residuals 20000 10000 0 -10000 t-ratio 8.14 17.6 P-value