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Study Tne I0p MBA programs attemptedpredict the average starting salary (in OOO"s) of graduates 0l the program based on the amouni o (uitlon (In $1000"s) ...

Question

Study Tne I0p MBA programs attemptedpredict the average starting salary (in OOO"s) of graduates 0l the program based on the amouni o (uitlon (In $1000"s) charged bY Ihe program and the averaqe GMA score the program students. The results o regression aalysis based 0n & sample / 75 MBA programs shown belov;Least Squares Linear Regression SalaryPredictor Variables Coefficient Sid Error VIF Constant 203.402 6573 3.94 0.0002 G mat 0,39412 09039 4,36 0,O000 Tultion 0.92012 0.17875 5.15 0

study Tne I0p MBA programs attempted predict the average starting salary (in OOO"s) of graduates 0l the program based on the amouni o (uitlon (In $1000"s) charged bY Ihe program and the averaqe GMA score the program students. The results o regression aalysis based 0n & sample / 75 MBA programs shown belov; Least Squares Linear Regression Salary Predictor Variables Coefficient Sid Error VIF Constant 203.402 6573 3.94 0.0002 G mat 0,39412 09039 4,36 0,O000 Tultion 0.92012 0.17875 5.15 0.0000 The mode was then used credie 950 contidence and prediclion Intervals Ior Y and for E(Y) when the (uition charged by the MBA program was {75.000 and (he GMAT cote was 675. The resuIbs = shown here: 9593 conlidence inlerval Ior E(Y): (126.610. 136,6401 95%a prediction interval for (90,113,+173,160) Which of the following inlerpretations correci want to use (he model to estimate E(Y)or all MBA programs= A) We are 959 confident that the average starting salary for graduates 0f = single MBA program that charges $ 75,00D tulllon and nas an average GMAT score 0 675 wili (all between 1126.610 and 136,640. 0) We are 95"0 conlidant Ihat (he Lrjo slarling salary Ior graduates 0 = singla MBA program that charges 75.000 tulllon and has an average GMAT score 0 675 wiii Iall between 190.13and /173.16.30. We are 9598 conildent Ihat the average o/ all starting salarles Ior graduates of ali MBA programs Uhat charge 575,000 tulllon and have A0 averago GMAT scord 0i 675 wiil fall belwoun 126.610and ,136.640, D) We are 95"e contident that the average of all starting salarles Ior graduates of all MBA programs that charge $75,000 In tultion and have an average GMAT score 0 675 will fall botwuan $90,113 and !173.16,30 Answer Ina quastlon Tcue or Falsa, 12 The conlldence Interval for Ihe moan Ely) marrowar that Iha prediction Intarval for ya Truo BI Fulse Solve tha problom Considar Ihe Interacilon modol E(v) 36+ |,2*1 2 4*2 2*1*2. Detarmlne Uha chanqe In E(y) whon *| changod Irom 6 to and *2 held Mxed a Ai1.8 B) 10.8 Ci11 01 42



Answers

Out-of-state tuition and fees at the top graduate schools of business can be very expensive
However, the starting salary and bonus paid to graduates from many of these schools can
be very high. The following data show the recruiter assessment score (highest $=5 )$ , the.
out-of-state tuition and fees (rounded to the nearest $\$ 1000$ ), and the average starting
salary and bonus paid to recent graduates (rounded to the nearest $\$ 1000$ ) for a sample of
20 graduate schools of business $(U . S .$ News $\&$ World Report 2009 Edition America's Best
Graduate Schools).
$\begin{array}{l}{\text { a. Develop an estimated regression equation that can be used to predict the starting salary }} \\ {\text { and bonus paid to graduates given the recruiter assessment score. }}\end{array}$
$\begin{array}{l}{\text { b. Develop an estimated regression equation that can be used to predict the starting }} \\ {\text { salary and bonus paid to graduates given both the recruiter assessment score and the }} \\ {\text { out-of-state tuition and fees. }}\end{array}$
$\begin{array}{l}{\text { c. Is the estimated regression coefficient for the recruiter score the same in part (a) and }} \\ {\text { in part (b)? Interpret the coefficient in each case. }}\end{array}$
$\begin{array}{l}{\text { d. Suppose that we randomly select a recent graduate of the University of Virginia }} \\ {\text { graduate school of business. This school has a recruiter assessment score of } 4.1 \text { and }} \\ {\text { an out-of-state tuition and fees of } \$ 43,000 . \text { Predict the starting salary and bonus for }} \\ {\text { this graduate. }}\end{array}$

So the media starts in celebrate for a new law. School graduates is giving any question about giving on the all sides the medium A said LS City score for the graduating class GPS, the media and Colin G. P. A. And the lights level is the number of volumes in the last school library. And, of course, a no, of course, of attending law school. The rank is in law school ranking I want is the best. So the first question themselves to explain why we expect be five to be less than or equal to zero. So we expect the five less than less than zero because because B five represents the sensitivity of salary, um, to law school ranking and it's rank off law school goes I the UN median starting salary for law school graduates. So the, um, the the sorry for law school graduates decrease as the rank goes I and as low rank being the best. So due to this invest relationship between the salary in the bank, the corruption of rank be five will be negative, so to be less than zero. So, in essence, there is on a bus relationship between salary around, so be five b negative. So the next question what signs do you expect for the other slow parameters and justify your answers so we can expect that be one will be positive because the media l a city score for the graduating class increases ancillary also increases. So be one will be positive because ls it is cause I'm salary of graduates increases so be one would be greater than zero now beat. So what's the real positive? Because as a college mignon GP increases the salary increases. So so as the media and increase its celebrity of graduates increases. So be to be positive on beat three to be positive, because if there are more volumes in the library, there is more chance of getting a higher salary. So be three with good and zero more volumes in the library. Pleased to if I asked salary. So Big Three be good on zero on before we go to an zero. If an all cost is high on a more fancy, this isn't giving. Therefore, students who have better chances are to me I a salary. So before we got on an zero, okay, Yeah, because I, uh a no cost fleets Sue. I have salaries so be for its return. Zero but be five is less than zero due to the first parts. We explain because the inverse relationship between the salary and drank so moving on to the next question. Yeah, usually in data in the laws School 85 the estimated in question is giving Yes, metal equation is giving on what is predicted Satirist Power parables Difference in salaries for schools with the random with a median GP different by one point. So the pretty dead Seri cafeterias parables different inside I was of school, the media ngp by one point would be so the coefficient off GP on This is because 0.248 on 24.8%. So as the confidence of percentage as cooperate off g p a is equals represents change in salary divided by any changing GP. So Yeah, sir, Coefficients off G p a is the presents change in salary developed by the unit change in GP Some of your answer The next question Interpret the coefficients on the variable log live life volume. So the coefficients on it very beatable. So the corrections will be the percentage change in salary divided by the presented change in the lifeboat. So this means that I'm going to be the presented changes. So I reduce the presented change alive. Oh, in library volumes. So you represented sensitivity of the library volumes, so this means library volumes Xu salary. Now, the next question would you say that it is better to attend a higher round law school? How much is the difference in ranking off 20 words in terms of predictive starting salary. So the answer would be no. It is better to attend low around law school instead of the higher around law school because is an inverse relationship between the rank of law school and the salary. So, yeah, attending e have rank law school in the Pappas off anymore. You'd be any less so the difference is rocking of 28 times, so no, it is better. So I send lower rent law school because days on universe relationship between the school. Yeah. Oh, little work off law, school and salary. So the difference in making 20 what items of predict a starting salary you beat 20 months applied I minus 0.33 and as the cost to minus 0.66 or minus 6.6 percentage. So due to difference in ranking or 20 in 20 um, salary decreases by 6%. So if the rank is lower by 20 units, then salary would be 6.6% ia so, so salary decreases by 6.6%. But if rank is lower, but it's what is the unit? Then salary for celery attained will be 6.6% IA does that answer?

We are looking at 30 pairs, first thing that we're gonna do is a paired T test. We're going to sum up all the differences and divide by the number of pairs which is 30. So what we get here is going to be approximately 15.267 Yeah. And we'll probably just say 15 to 7 for simplicity are non hypothesis. Is that the mean difference is zero? And since we're trying to find if there is a difference that means that we are conducting a two tailed test so does not equal zero as our alternative hypothesis. And then we get down to the T statistic but we calculate that bad boy and this is going to be equal to D. Bar which is 15 to 7. And I forgot to do this guy right here. S. D. SD is going to be 6.374 Mhm. And we'll go ahead and put that number up there. So we got D. Bars 15 point oh 27 minus heroes. We'll just keep it like that actually. We'll just put it there. And then we got our SD which is 6.374 divided by the square root of the sample size. Our sample sizes 30 or our number of pairs. Our degrees of freedom is going to be one less than the sample size. So 29. And we can go to table forward to find out that critical value and we find out that it is two point oh 45 Since we are looking at a T. Value or T here T 450.0 point 025 Since we're looking at a significant level of 5% it's a detailed tests. We gotta split that 5% on two tails and that critical values to 45 This calculated value right here is about 12 and this is going to be clearly outside of that. So therefore at the 5% significance level we can reject the null hypothesis and conclude that there is a difference in means. Mhm. At the 1% significance level we have critical value of 2.756 which once again at the 1% significant subtle we will reject the null hypothesis since it's still nowhere near 12. Now I think we're asked to creates a construct a 95% confidence interval and it's going to be given by this formula right here. So what we can do is just plug in those values as before our D. Bar is 15 point oh 27 Yeah. Plus or minus that T statistic right here. Which is keep 245 Yeah. Mhm. Sometimes SD got to keep scrolling at 6.374 divided by the square root of the sample size herb pairs. So we got 30 right there. So for a lower bound we're gonna get 12.65 Mhm. Just 17.1 I believe. 17.41 Mhm. And that right there is our 95% confidence interval. Mhm. Now for the next part were asked to do some normality checks. Actually, before we do that, compared to example 10.4 on page 4 45 we find that this confidence interval right here is actually narrower and then we can make some box plots, normal probability plots. Um And eventually what we find is that the box plots are normally shaped at least nicely distributed with no outliers and that the normal probability plot is approximately linear, which therefore means normal and therefore it is going to be reasonable to do a T. Test.

But one this is the estimated equation. The usual S standard errors are in green and in round brackets. The hetero skid elasticity, robust standard Iran's are in blue and in square bracket. As you can see the robot standard Iran's are somehow larger in all cases on variable lock of E. X. B pp. Yeah the robust T statistic is 1.5 not too high. So we are not very convinced if performance its link to spending hard to. The f statistic has a value of 132.7 and a p value almost zero. Therefore there is the strong evidence of heterocyclic elasticity for three and four. This is the same equation estimated by weighted least square usual. Standard herons are in round and green brackets and weighted least square standard Iran's are in blue square brackets. We don't care about it. Their standard barrel over there. Constant term the intercept. So I don't report the centered errol oh, weighted least square for it. Yeah. Oh sorry the round one hour the usual wait at least square and the square one is robust. Type all part three. Mhm. We have to compare the estimates from weighted least square approach to L. S. Approach. Yeah. And we see that the old L S n W L. S coefficients on lunch or the same. But for other variables they differ. The waiting list square estimate on lock of spending is much larger than the old L. S coefficient. Based on this estimate a 10% increase in spending. Let me write that down. That is equivalent to an increase of 0.1 in lot of spending. Let's do you a pulling 65 percentage point increase in the math past rate the weighted least square T statistic is much larger too. Before we get 1.5 now we get 3.8. More than double past four. We compare the robot standard Iran's with the usual W. L. S. Standard Iran's and we find that for the key variable lack of spending, the robust standard error is somewhat larger than the usual one robust scented errol, our lock of enrollment also somewhat higher and for lunch, the robust version is slightly lower than the usual one, part five, the weighted least square estimated is more precise and by precise, I mean, robust standard errol is smaller than the robust version of the old LS estimate. For the first one we got 1.82 and for the second one two point 35


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