In a simple linear regression problem with n = 28, the following estimates were obtained:

beta0= 4.30, beta1= 0.56, sd{beta0} = 0.012, sd{beta1} = 0.034, sigma = 0.1385

Xbar = 0.0773, SSX = 14.598.

Values of X were in the range 1.43 to 0.683.

(a)Write the simple linear regression model.

(b)Write the estimated regression line and the estimated error variance.

(c)If appropriate, estimate the mean value of Y for the given X values below. If not appropriate, say why.

1. X = 0.
2. X = 2.

(d)Give a 95% confidence interval for the slope of the regression line.

(e)Give a 99% prediction interval for the next value of Y when X = 0.5.