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Use the data in ATTEND for this exercise.(i) Obtain the minimum, maximum, and average values for the variables atndrte, priGPA, and ACT.(ii) Estimate the model$$=\beta_{0}+\beta_{1} \text { priGPA }+\beta_{2} A C T+u$$and write the results in equation form. Interpret the intercept. Does it have a useful meaning?(iii) Discuss the estimated slope coefficients. Are there any surprises?(iv) What is the predicted atndrte if priGPA$=3.65$ and $A C T=20 ?$ What do you make of thisresult? Are there any students in the sample with these values of the explanatory variables?(v) If Student A has priGPA $=3.1$ and $A C T=21$ and Student $B$ has priGPA $=2.1$ and $A C T=26,$ what is the predicted difference in their attendance rates?

(i) see solution(ii) $\widehat{a t n d r t e}=75.70+17.26 p r i G P A-1.72 A C T$(iii). As priGPA deals with presentation in college, while $A C T$ is a degree of potential in college, thus it can see that those students who had more prospective think that they can get good percentageeven by missing lectures.(iv) $[04.299]$(v) 25.86

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Chapter 3

Multiple Regression Analysis: Estimation

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I don't know everyone we have. Ah, question number four. Computer exercise in just a tree. He's a data attend for the exercise. The first question is asking, Obtained whenever trail use for the variable 10 drainage pre G p a in a C t. And I'm using status. Just put this comment. Summarize, Attend rate three gp and a C t. And it gives me this table. So we see that What? A 10 Right? The minimum demonstrated, like 6.25 a maximum of one person. And the average attendance rate is like 81.70 for pre jeep. A word of the GP prior to turn, the minimum is 2.85 and the maximum is 2.9 tree and the average G p a private term in this simply to 0.58 on for a C. T. Changed from turkey to Turley. So did you. On the average is 22 points. 51. So, uh, this is the first part. All right. This is part of a black eye. No, I have a second part. Okay, um, for this part, we are asked to estimate the model that is attend Great tennis very is equal to bait of Europe. One state of one pgp a prospector too a c t. So just what I do is instead a progress Kendry to PGP and 82 Come in tonight on Did you see that? Did you know the coefficients? Constance, if you debate out zero the coefficient on pretty pay, which is a solemn estimates and a CT. Right? So the coefficients are square here and we have a simple we're here, so I'm just gonna write this out. So from dis aggression we get, we get he estimated attendance rage is equal to bait a zero to the constant 75.7. Tough beta one, which estimates in 17.26 one hat G p A and beta two had no asked for beta 2/2 days. Mining 1.71 minus 1.70 wound times a CT. So, uh, Okay, that's interpret to you. Questions interpret intersect. What? That is constant. 75.77. So what is the interpretation from this? This is if pre VP is your and a c T zero damages tim's asses, can't you? So the estimated attendance rate for students who had the DPL steel And who has in a beauty school serious. 75.7 with this. Is this meaningful? Uh, maybe not really. Because get the, uh, some statistics. Fine. The minimum three g p. A is 0.85. Some cannot really have. Like, you're here. And minimum a CT is touching, so we don't We don't have any simple needle and hero. Okay? All right. Um, so the term part of this question is asking us to discuss the estimated slope coefficient. Are there any surprises? So beta one on base, too? We okay, so Beta one. But no one had its 17.26. What could this mean? This means holding the city school and increase of one unit in p g p a. It's gonna increase. Get him in shape by 17%. This is what it means. Can't complain. 26%. An increase of keep a buy. One point when a beauty's fixed increases the chemistry by 17%. And the debate that you had is mine. It's 1.71 which is we've been interpreted as only kissed the previous Page six and increase. 01 point in the city score decreases the account by one person, only 1%. And are there any surprises? The coefficients is kind of surprising to another negative, uh, corporations on the city school kind of expect when the city school goes up. 10 states Trudeau succulent. All right, The fourth parts is asking us what is predicted attendant trade if the pre g p a 3 65 and a seed school 20 So we just kind of put you just use this formula here. A p g p a will prove stripper 65 um, for a CT will put 20 on this is gonna give us when we do the calculations. Your attendance rates when we have GP off 3 65 and 80 school 20. The estimate is 104 points. Pull in 99. What do you make of this result? It's asking us. So we know that attendance rate cannot be higher and 100% on impacting date ages the mountains 100% but this is just like a model gives us an estimate 4.5, which is out of the range of possible values. But you can see it in action can take. Let's remember that this is just estimate that is coming out of the model that we have. Another question is, Are there any students in the temple with values of the extra naturally valuables? There's a fact students with a pre detail 3 65 on a 20 the attendant straight off that student is 87.5. So the actual I'm straight with a GPS 3 65 and 20 87.5. But the estimates that is coming out of the model is 100 and 4.5. Okay, so question is, if student A has pre deviate off 3.1, Okay, student has cream kee p A p 0.1 and any seat you on 21 then student B has a pre G p. A. Uh, two point wound on has been a ski school of 26. What is the predicted difference in the temples? Rage. So we're just gonna so the particular difference down kept that chemistry is just gonna be the cardinal is gonna disappear 17.26 times down. Top three G p A minus 1.7. I want a c t man. So the predicted difference in the attendant trade Oh, is gonna be 17.26. Time's different to me, G p a. There's been a court like defense and taking from B j p g p A b no Miss pdp a subsequent lineman's checkpoint one I minus 1.71 times down to a T. T. The folks in a city 26 minus 21 on this gives me the result is minus 20 five point a key one So and this waas So this one, the estimated attendance called B minus estimated attendance for a Okay, So our expectation is Shouldn't be it's gonna have the attendance rate nor by 25.1%. Stan Student, eh? Okay. All right. Hope that Holmes, Thanks for watching

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