*** Indicate if statement is true (T) or false (F), andexplain why? ***

(a) A 95% prediction interval for a futureobservation at x0 is wider than the 95%confidence interval for the mean response atx0.

(b) For a simple linear regression model y = β0 + β1x + ε, andusing a 95% confidence interval for the slope β1(-0.0416, 0.8145), we can conclude in a 0.1 significancelevel that x and y are not significantly linearlyrelated to each other.

(c) The coefficient of determination R^2 isalways a good measure of comparison between twomodels.

(d) The estimator σ^2 = MSE has a normaldistribution.

(e) A 95% confidence interval for the slope β1 will bewider if we have a sample size of n = 11 insteadof n=7

(f) In a simple linear regression model, where the errors areindependent and normally distributed, the leastsquares estimator β0 has a normal distributionalso.

(g) The prediction is trustworthy even if weare in the region where the values of X areextrapolated.

(h) The residual is the difference between theobserved value of the dependentvariable and the predicted valueof the dependent variable.

(i) If the p-value for testing H0 : β1 = 0 Vs H1 : β1 ̸= 0 isless than the significance levelα, then wereject the null hypothesis and conclude that thereis no significantlinear relationship between x andy.