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The following estimated regression equation was developed for a model involving twoindependent 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}

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a) $\hat{y}=42+9.01 x_{1}$b) Thus the presence of multicollinearity causes the coefficient of $x_{1}$ to differ in the two models.

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Temple University

Missouri State University

Cairn University

Idaho State University

Lectures

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02:15

The following estimated re…

The estimated regression e…

09:55

1. The estimated regressio…

2.2. Refer to Exercise 11.…

Now, given both of these regression models, one of which is a multi variable having two independent variables X. One and X two And the other one, X 2 is discarded. And we simply use X one tomato. A certain phenomenon With a regression model. Now we may notice that the values for X one are different in each of these cases. When X two is present, it's 8.63 And when X two is removed We have 9.1. Now the interpretation behind this difference, it's simply that for the case that there is a single variable in the regression model, the coefficient of the independent variable gives us an estimate of the change and why or the control variable given a one unit change in the independent variable X one. For example, if we increase the value of X by one, we can expect the estimate of why to go up By 9.01. Very well now, what about the multi variable case? The coefficient of X one represents an estimate of the change and why For a unitary change in X. one when all of the other variables are held constant. Now noticing the differences between the coefficients in each case is what can be attributed to this difference. Now, multiple in Merete is the occurrence of inter correlations among two or more independent variables in a regression models such as this. So multi culinary T can lead to misleading results when attempting to determine the influence of individual variables, and for that reason it's better to employ variables that are independent from each other. They are not correlated or dependable in any way.

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