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Use the data in ATTEND for this exercise.(i) In the model of Example $6.3,$ argue thatUse equation $(6.19)$ to estimate the partial effect when $\operatorname{priGPA}=2.59$ and atndrte $=82 .$ Interpret your estimate.(ii) Show that the equation can be written as where $\theta_{2}=\beta_{2}+2 \beta_{4}(2.59)+\beta_{6}(82) .$ (Note that the intercept has changed, but this is unimportant.) Use this to obtain the standard error of $\hat{\theta}_{2}$ from part (i).(iii) Suppose that, in place of priGPA(atndrte $-82 ),$ you put $(p r i G P A-2.59) \cdot($atndrte$-82)$ Now how do you interpret the coefficients on atndrte and priGPA?

i) $-0.092$ii) $\hat{\theta}_{2}$iii) $\theta_{0}+\beta_{1} a t n d r t e+\theta_{2} p r i G P A+\beta_{3} A C T+\beta_{4}($priGPA$-2.59)^{2}+\beta_{5} A C T^{2}+$ $\beta_{6}($ priGPA $-2.59) \times($atndrite$-.82)^{2}$

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Chapter 6

Multiple Regression Analysis: Further Issues

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correct one. If we hold all variables except priority g p A and use the usual approximation of the change in priority. G p A square is twice Priore g p a. Times to change in priority g p a. Then we can rewrite the change in students final. Great as follows. It should be beta too, plus two beta, four times prior G P A plus beta, sixth times attendance rate and altogether, times the change in priority B A. But what we care about is their this ratio instead. So I will divided both sides for the change in Priore g p a. Now we can plug in their numbers we got from Equation 6.19 that's we have a tattoo, but that you had equals minus 1.63 beta forehead equals 0.296 and beta six hat equals point. 0056 So when prior G P. A. Is 2.59 and attendant rate is 0.82 we can can too late this ratio. Okay, we just need thio pluck all these numbers into the right hand side of the equation and what you would get is so all of these with equal or approximately equal minus 0.0 nine to. And that is part one of the question for part two. Part two is straightforward now from the previous equation, you can easily derive that they talk to you equals beta two plus beta. Four should be to beta four times, 2.59 plus beta six times 82 and we can calculate their standard error of Seita. Had to be, Oh, you will have data to hat equal minus 0.91 and the Senate. Errol of Feta to Hat is 0.363 This implies a very small T statistic. Four. Fated to hat. Remember, the T statistic formula is say that you had or any estimated coefficient divided by the standard error of their estimated coefficient. All right, now, Part three. The question here is suppose that in place of Priore GPA Times attendant rate minus 82 you put prior G P A minus 2.59 times attendant rate minus 82. So how do you interpret the coefficients here? Well, four prior G p. A. It's coefficient should show the effect mhm of prior G P. A. When this variable changes from the level 2.59 mhm and you would do the same for attendant rate, it had a It has a similar meaning. It is three effect of attendant rate when the raid either increase or decrease from the level 80 to you.

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