You fit two models in a situation where there are two groups, represented by the dummy variable d, and a potential covariate x. Explain the difference in the interpretation of the parameter β1 in the...

You fit two models in a situation where there are two groups, represented by the dummy variable d, and a potential covariate x. Explain the difference in the interpretation of the parameter β1 in the two models.

Model 1: y + β₀
+ β₁d + ε Model 2: y = β₀
+ β₁d + β₂x + ε

Table 11.15 summarizes the results of a regression of a variable Y on two independent variables X1 and X2. There were 35 observations in the data.

(a) Give a point estimate of L = β_o
+ β₁
- β₂:

(b) Give a 95% confidence interval for this quantity.

(c) Does including X2 in the regression significantly improve the prediction of Y?