Economics/Statistics

5.9.) To find out if there is any relationship between teacher's pay and per pupil expenditure in public schools, the following model was suggested: Payi=β1+ β2
Spendi +ui,  where Pay stands for teacher's salary and Spend stands for per pupil expenditure.


a.) Plot the data and eyeball a regression line.
b.) Suppose on the base of  "a.)" you decide to estimate the above regression model. Obtain the estimates of parameters, their standard errors,  r², RSS, and ESS.
c.) Interpret the regression. DOES it make economic sense?
d.) Establish a 95% confidence interval for β2. Would you reject the hypothesis that the true slope coefficient is 3.0?
e.) Obtain the mean and individual forecast value of Pay if per pupil spending is $5000. Also establish 95% confidence intervals for the true mean and individual values of Pay for the given spending figure.
f.) How would you test the assumption of the normality of the error term? Show the test(s) you use.