## Related questions with answers

Look back at the previous exercise.

The prediction equation from fitting the multiple regression model equals $\hat{y}$ = 12 + 6$x_1$ + 3$x_2$. Use this equation to find the predicted population means for each group.

Solution

VerifiedGiven:

$\begin{aligned} \hat{y}&=12+6x_1+3x_2 \\ &\textcolor{#4559AC}{\text{Result previous part:}} \\ x_1&=\left\{\begin{matrix} 1, &\text{ if category 1} \\ 0, &\text{ otherwise} \end{matrix}\right. \\ x_2&=\left\{\begin{matrix} 1, &\text{ if category 2} \\ 0, &\text{ otherwise } \end{matrix}\right. \end{aligned}$

We need to determine the predicted population means for each group.

The predicted population means for a group is obtained by evaluating the prediction equation at the corresponding values of $x_1$ and $x_2$.

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