In Minitab, open the SAT10 data from Blackboard. There you will see recorded for each of the 50 US States their average total SAT score (math + reading) for a recent run of the test along with the average salary of its teachers. (and some other variables we will consider in later chapters). We wish to construct a regression model to predict Avg. Total Score from Avg. Salary.

Carry out the requested regression analysis using Minitab (except for the few requested by-hand calculations) and answer the associated questions. Copy and paste all relevant Minitab output into your homework paper.

a. Using Minitab, compute and interpret the correlation between Avg. Total Score and Avg. Salary.

b. Create a scatterplot of Avg. Total Score vs. Avg. Salary with regression line. With Minitab, compute the basic statistics needed to compute the equation of the regression line, then compute the equation by hand. (Include the Minitab print out of the basic statistics used in your computation and type the equation itself, but, remember, you do not have to include your by-hand computations in your paper.)

c. Using Minitab, do a complete regression analysis of this data including:

-A Model Summary

-The Regression Equation

-The Coefficients Table

-Fits and Diagnostics for unusual observations

-Storage of Residuals (Do not copy and paste the residuals to your paper.)

-Diagnostic graphs

d What is the percentage of variance of the Avg. Total Score variable explained by this linear relationship with Avg. Salary? Briefly explain your answer.

e. Interpret the slope of the regression line for this model.

f. -. Consider the t test of the slope. How many degrees of freedom are used for this t test?

-Show that the T-value is equal to the slope divided by the standard error of the slope. Briefly explain why this is so.

-Assuming it to be valid, interpret the result of the t test of the slope. Under what conditions is it valid?

-Compute and interpret a 90% confidence interval for the population slope.

g. Perform an Anderson-Darling test on the residuals of this regression. Copy and paste the Minitab output for this test to your paper. What conclusion do you draw from it about the Normality Assumption?

h. Which of the 3 Diagnostic Graphs is used to assess whether the standard deviation of the residuals is constant?

i. Use Minitab to compute and interpret (assuming them to be valid) 95% confidence and prediction intervals for Avg. Total SAT score for a state in which average teacher salary is $40,000. Under what conditions are your interpretations valid?