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$$\begin{array}{c}{\text { Refer to exercise } 5 .} \\ {\text { a. Use } \alpha=.01 \text { to test the hypotheses }} \\ {H_{0} : \beta_{1}=\beta_{2}=0} \\ {H_{\mathrm{a}} : \beta_{1} \text { and/or } \beta_{2} \text { is not equal to zero }}\end{array}$$$y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\epsilon,$$$\begin{array}{l}{x_{1}=\text { television advertising }(\$ 1000 \mathrm{s})} \\ {x_{2}=\text { newspaper advertising }(\$ 1000 \mathrm{s})}\end{array}$$\begin{equation}\begin{array}{l}{\text { b. Use } a=.05 \text { to test the significance of } \beta_{1} \text { . Should } x_{1} \text { be dropped from the model? }} \\ {\text { c. Use } a=.05 \text { to test the significance of } \beta_{2} . \text { Should } x_{2} \text { be dropped from the model? }}\end{array}\end{equation}

a) Therefore, there is significance relation between the amount of television advertising and weeklygross Revenueb) Therefore, we can conclude that $\beta_{1}$ is significant and hence the television advertising $x_{1}$ should not be dropped from the model.c) Therefore, we can conclude that $\beta_{2}$ is significant and hence the Newspaper advertising $x_{2}$ should not be dropped from the model.

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Piedmont College

Cairn University

Idaho State University

Lectures

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we're told to refer to exercise five, which basically gives the gross revenue in terms off the TV advertising and the newspaper advertising. So this is the why variable and these air the tube X variables. So first, let's get our multiple regression equation. So to do that, we put in our input wide range just basically these values. And then we put in our input X range, which is these two columns keep the labels. We set our confidence level to 99% because we hard casting testing at the significance level off Coast Point or one for the output range. We're going to put the output here, So let's click OK and get our multiple linear regression equation. So we have our statistics. Here we have the r squared and then we have the regression and residual over here, the F statistic and the coefficient. So let's look over these values. So in part they were basically asked Alfa equals point or want to test the hypothesis that at least one of the parameters is not zero. So we CRF statistic here. So I've statistic is 28.38 So looks like that down we also see our P value for but the now hypothesis. So we have the P value for a tous steak for this hypothesis. So we see this p values 0.1 which is less than point for one. So we can reject the null hypothesis and conclude that the relationship this significant to reject now hypothesis where you can ship. Please, sweetie. Now for Part B were asked to use our Michael's 0.5 to test the significance off pita one. So paid a one corresponds to television advertising. So you know, one which is the coefficient. It's right here. So when I put in, they had a one. Then let's look at our A T statistic and the value so we see that value is point or six 53 So I'm gonna put that in here. So, uh, thieves value is 0.653 So that's less than 0.5 Again, we can reject now hypothesis, and we can conclude that Data one is significant. Okay. And next one should not Detroit from the model. Now let's look at data to so here appear to which is the coefficient for newspaper advertising. It's 1.3. We're gonna go ahead and look at our P values for few values. 0.9 Yeah, which is to less than a 0.45 So again, we reject our hypotheses. You conclude the Beta two is significant in this model on next to should not think dropped. And so, from all of the values given here with the T statistic, P statistic, statistic and the value over here, these are our answers to the question, I mean.

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