Nicholas Vasconcellos, Tutor at Instituto Federal do Espirito Santo (IFES), Numerade Educator

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Essentials of Modern Business Statistics

The following estimated regression equation was developed for a model involving two
independent variables.
$$\hat{y}=40.7+8.63 x_{1}+2.71 x_{2}$$
$$\begin{array}{c}{\text { After } x_{2} \text { was dropped from the model, the least squares method was used to obtain an }} \\ {\text { estimated regression equation involving only } x_{1} \text { as an independent variable. }} \\ {\hat{y}=42.0+9.01 x_{1}}\end{array}$$
\begin{equation}
\begin{array}{l}{\text { a. Give an interpretation of the coefficient of } x_{1} \text { in both models. }} \\ {\text { b. } \text { Could multicollinearity explain why the coefficient of } x_{1} \text { differs in the two models? If }} \\ {\text { so, how? }}\end{array}
\end{equation}

Chapter 13: Multiple Regression