The multiple linear regression model y 0 lxl 2x2 3x3 is fitted to a data set with n 15 observations, and the parameter estimates 0 65 98 1 23 65, 2 82 04, and 3, 17 04 are obtained (a) What is the fitted value of the expected value of the response variable when x1 1 5, x2 1 5, and x3 2 0 (b) If the...

The multiple linear regression model y = 0 + lxl +2x2 + 3x3 is fitted to a

Question:

The multiple linear regression model
y = β0 + βlxl +β2x2 + β3x3
is fitted to a data set with n = 15 observations, and the parameter estimates β^0 = 65.98. β^1 = 23.65, β^2 = 82.04, and β^3, = 17.04 are obtained.
(a) What is the fitted value of the expected value of the response variable when x1 = 1.5, x2 = 1.5, and x3 = 2.0?
(b) If the fitted value from part (a) has a standard error of 2.55, construct a two-sided 95% confidence interval for the expected value of the response variable at this point.