Question1. Consider the following multiple linear regression equation: $$Y^{\prime}=2.75+13.42 X_{1}+.75 X_{2}-4.21 X_{3}+10.30 X_{4}$$
Find the predicted value of the dependent variable $(\hat{Y})$ given the following situations: a. The values of all the independent variables are equal to 0 . b. $X_{1}=2 ; X_{2}=3 ; X_{3}=1 ; X_{4}=-3$ c. $X_{1}=-1 ; X_{2}=3 ; X_{3}=-1 ; X_{4}=8$

Studdy Solution
Substitute $X_1 = -1$, $X_2 = 3$, $X_3 = -1$, and $X_4 = 8$ into the regression equation:
$$\hat{Y} = 2.75 + 13.42(-1) + 0.75(3) - 4.21(-1) + 10.30(8)$$
Calculate the result:
$$\hat{Y} = 2.75 - 13.42 + 2.25 + 4.21 + 82.40$$
$$\hat{Y} = 2.75 - 13.42 + 2.25 + 4.21 + 82.40 = 78.19$$
The predicted values of $\hat{Y}$ are: a. $\hat{Y} = 2.75$ b. $\hat{Y} = -3.27$ c. $\hat{Y} = 78.19$