In a data set with n = 50 observations, you try fitting two models: Model 1: y = β 0 + β 1 x 1 + β 2 x 2 + ε, giving SSE 1 = 256, Model 2: y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + ε, giving SSE 2 = 194...

In a data set with n = 50 observations, you try fitting two models: Model 1: y = β₀
+ β₁
x₁
+ β₂
x₂
+ ε, giving SSE₁
= 256, Model 2: y = β₀
+ β₁
x₁
+ β₂
x₂
+ β₃
x₃
+ ε, giving SSE₂
= 194 and β₃
= 2:1.

(a) Calculate the F statistic for the null hypothesis that x₃
is not related to y, after controlling for x₁
and x₂. Interpret the result.

(b) Calculate the t statistic for the coefficient for x₃
and interpret the result.

(c) Using your result from part (b), calculate the estimated standard error for β₃
= 2:1, then construct a 95% confidence interval for β₃.