The data are annual disposable income and total annual consumption for 12 families selectedat random from a large metropolitan area. Regard annual disposable income (INCOME) as theexplanatory variablexand total annual consumption (CONS) as the dependent variabley. Usingthe software SAS to conduct the linear regression ofyonx, answer the questions that follow. Thedata and SAS codes can be found on Canvas. By specifying appropriate options in the MODELstatement of PROC REG, the answers to all questions below can be directly found from the SAS outputs. Required:
a. What is the least squares equation?
b. What percentage of the variation in CONS has been explained by the regression?
c. Construct a 95% confidence interval for β1.
d. Conduct a test to determine if β1 is significant at the .05 level of significance. Use two methods: t- value and p-value.
e. Find the estimated standard error of the model s
f. Find the predicted value ofCONS for INCOME = 35000.
g. Construct a 95% confidence interval for the mean value of CONS for INCOME-35000.
h. Construct a 95% prediction interval for a new observation of CONS for INCOME = 35000.