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Use the data in GPA1 for this exercise.(i) Add the variables mothcoll and fathcoll to the equation estimated in $(7.6)$ and report the resultsin the usual form. What happens to the estimated effect of PC ownership? Is $P C$ still statisticallysignificant?$$\begin{array}{l}{\text { (ii) Test for joint significance of mothcoll and fathcoll in the equation from part (i) and be sure to }} \\ {\text { report the } p \text { -value. }}\end{array}$$(iii) Add $h s G P A^{2}$ to the model from part $(\mathrm{i})$ and decide whether this generalization is needed.

The $p$ -value of the coefficient of $h s G P A^{2}$ is 0.115 which is greater than the critical p-value of 0.05at 5$\%$ level of significance, indicating that the generalization by adding $h s G P A^{2}$ is not needed.

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Chapter 7

Multiple Regression Analysis with Qualitative Information: Binary (or Dummy) Variables

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Ray L.

June 5, 2021

How can i put the hsGPA on R studio?

Dylan L.

November 7, 2021

Hello Are we able to see the video for the coding of this in STATA?It would be much appreciated!

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the first thing we want to do in this problem is ah, at the variables moth call and fault call to the equation. And 7.6, um, and then report our results in the usual form, which is just a regression table. So what we're interested in seeing is what is the change of, um, adding these two variables to PC and is PC still see justice tickly significant. So what I've done is I've added these I've done these regressions and are you could do them in, uh, Eve. Use python state of whatever programming language you want. And, um, I've computed the regression results. So in PC PC for our first model is equal to 0.57 approximately. This PC in our second model is equal to zero point 05 nine about so there's not much of a change. There's a slight change. How would you test this? You would ah, probably do a test to see if the beta values on these variables change. The coefficients on these values have changed. But what we do see is that there is a change in the significance level. Um so the P value for our first PC is equal to 0.7 about in our second model, it's equal to 0.1 So it's still statistically significant at the 0.5 alfa level. But it depends on what you set your outfit would be. If it is that, then great, You don't have anything to worry about. But suppose you change your significance level from 0.5 to 0.1 then in the second model, it would no longer be statistically significant. But that shouldn't really be that big a problem, because it wouldn't be statistically significant in the first model either. That's a pretty harsh alphabet you to take on. So, um, this question s o the estimated effect of PC ownership, it seems like it goes up a little bit. And then, um, is PC still statistically significant at the Alfa level of 0.5? Yes. So now what we want to do is see if there is a change in a significant joints or we want to test the joint significance of adding moth call and forth call into our model. So to do that, we would do an F test for the joint significance level. And this is the formula right here. It's simply the sum of squares of the air of the restricted model minus the sum of squares. Of the era of the unrestricted model, divided by queue and queue is a number of restrictions. So it's the number of variables in our larger model that's not in our smaller model. Okay, so, um, why should you guys these models before? So in our first model, we don't include moth call and father Call, but in our second model, we d'oh. So what we want to do is, um S O. R q would equal to. All right, Those are the only two variables that we don't have. Ah, the sum of squares of the error of our unrestricted model. We'll get to in a second. Our end is equal to the number of observations we have. We get that by since we have a complete data set, we look at the number of rows we have, and in this situation we have 141 observations. Our kay is the number of independent variables in our model, and we have in our larger model. And we have 12345 five independent variables. So this is five, and then the one is there. So then now we have to find the sum of squares of the errors for both our models. So this first unova table. So we got these from the Innova tables. So this first Unova table is for our first regression model, and the sum of square of the error is the same thing as the sum of squares of the residual. So we find a residual, and then we find the column with the sum of squares, and we get this value of 15.1487 So this is 15.1 for 87 and then for our unrestricted model, which is our second model, um, we would do the we would find our, um, the sum of squares of our residual there. And that's down here. That's this value. Oh, yeah, that's that value. So we would replace this with hoops, see if I can move this back. How they begin. This is equal to 15 0.940 and our cue is, too, as we already discovered This is a sum of squares of the rip residual for our unrestricted model. This model down here is equal to 15.94 and we have 141 observations minus five. Okay. Minus five. Minus one. Too many colors, but near the idea. All right, This is how you would calculate rs statistic. And now we would find the p value. Um, and from this result, we get that r F statistic from down here are a statistic is approximately 0.24 and our P value is approximately, and it got cut out a little bit. Here. Let's see if we can move this. Yes. No. All right. Um, well, this value over here, that's now cut off is equal to, um let me get it for you guys real quick. 0.0 0.783 Um, or this is equal to one minus R p value. So our P value would be one minus 10.783 Oh, sorry. No, no, This is our p value. Our key value is 0.783 So because our P value is 0.783 which is so much higher um than our Alfa of 0.5 even 0.1 if we wanted to use that. This is insignificant. Um, doesn't really change the amount of variance we capture in our model. So, uh, to answer the second question, um, we test for joint significance. So ah, with an f statistic of 0.24 P value of 0.783 a and degrees of freedom of two and 1 35 1 35 You get one from 1 41 minus five minus one, which is 1 35 So this right here is 1 35 So with an F statistic of 350.24 p value 0.783 and degrees of freedom of two on 1 35 we find that the change in variants of joint significance of Moscow and fought call at the 350.5 significance level is insignificant or is not significant. And now, um, the last part of this question is adding the high school G p A. Ah, squared that the high school G p a square to the model and decide if this generalization is needed. So we have the results over here. So high school G p a squared. We see that, um, we have Ah, this variable down here. We have a insignificant ah code if the coefficient. So this at the 0.5 levels because 0.12 is greater than 0.5 We really don't need this generalization. Um, and we don't, uh, So I would personally not add high school G p a squared into this model.

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