Consider the simple linear regression model y = 10 + 30x + where the random error

Consider the simple linear regression model y = 10 + 30x + ε where the random error term is normally and independently distributed with mean zero and standard deviation 1. Use software to generate a sample of eight observations, one each at the levels x = 10, 12, 14, 16, 18, 20, 22, and 24.

(a) Fit the linear regression model by least squares and find the estimates of the slope and intercept.

(b) Find the estimate of σ².

(c) Find the value of R².

(d) Now use software to generate a new sample of eight observations, one each at the levels of x = 10, 14, 18, 22, 26, 30, 34, and 38. Fit the model using least squares.

(e) Find R² for the new model in part (d). Compare this to the value obtained in part (c). What impact has the increase in the spread of the predictor variable x had on the value?