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Out-of-state tuition and fees at the top graduate schools of business can be very expensiveHowever, the starting salary and bonus paid to graduates from many of these schools canbe 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 startingsalary and bonus paid to recent graduates (rounded to the nearest $\$ 1000$ ) for a sample of20 graduate schools of business $(U . S .$ News $\&$ World Report 2009 Edition America's BestGraduate 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}$

a) Salary $\&$ Bonus $=-20.02+33.73$ Recruiter Scoreb) $\mathrm{y}=0.88+14.6$ Recruiter score $+1.37$ Tuition feec) No, the estimated regression are different in part a and part b.d) 119.65

Intro Stats / AP Statistics

Chapter 13

Multiple Regression

Descriptive Statistics

Linear Regression and Correlation

Cairn University

Oregon State University

University of St. Thomas

Idaho State University

Lectures

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Out-of-state tuition and f…

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Situation P) Below are the…

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In exercise $6,$ data were…

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So in this question, we are given this Excel table that has a list of schools and basically has two ex variables one which is the recruiter. Score on the tuition and fees off thes schools in thousands of dollars. And the why variable or the dependent variable, which is the salary and the bonus. So the salary and the bonus that the students receive there's a function off the recruiter score off the school on the tuition and fees. So in the first part, we are asked to develop a regression equation that can be used to predict the salary, using just a recruiter assessment score. So for this equation, now, we have all of the data there. So we have all the recruiter scores over here, and we have all the salaries in column D. So let's use the stats to in Excel to get our regression equation. So we have our starts to pack and we're gonna use linear regression. So our input range here the wide range goes from deep one all the way up to the 21 which is over here and our X range for change that circles from T one 2021. And our X Range is the recruiter score. So it goes from V one to the anyone. So we're input X ranges. Be one. Make sure we get that to be 21. We want the labels to be there. We said the confidence level to be 99% and we start our output at 8. 23. So we start our output here. We keep everything else this way, and then we quick Okay. Which should give us our equipped linear regression equation off the salary in terms off the recruiters. Course. Let's look here. So here. So let's make sure our input range is correct. Okay, So checking. Yes, our input range is correct. Now we get the summary output, which will give us our equation. So if we go here, we see that the intercept is minus 20.2 and are coefficient for the recruiter scores 33 point seventies. So we're gonna take these values. We're going to write our equation. So we have. Why is equals to the intercept, plus the coefficient times recruiter school. Which gives us the answer to part a. Now, let's look at part B. So in part B were asked to develop the regression equation, given both the recruiters score and the heart of state tuition fees. So in part, be were asked told write the equation y in terms off both the recruiter score and the tuition fees. We're gonna go here, and we're gonna change our X range to both columns B and C, and we're going to put our output over here. So let's put our output himself. 24. Let's go ahead and compute. So we have our summary output here. So from our summary out. But we have our intercept for the equation, along with the coefficient for the recruiter score and the tuition fees so thes values will give us our multiple regression equation. So let's go ahead and write that equation for parties. So we have wise equal to the intercept plus coefficient off the recruiter score. I'm still include her score less preparation for tradition and peace and vision on and fees. So we have our answer to 5 ft over here now, in part, seeing were asked if the estimated regression coefficient for the recruiter score is the same for party and being so we see that the coefficient for the recruiter score for party 6 33 0.7 and the estimated reporter score sufficient for parties 14.5. So we say that they're not the same and were asked to interpret the coefficient in each case. So for interpreting the coefficient. So it's to that so far apart. A. Why increases bye. About 33.7 units on average, for an increase in one unit off recruiter scores. But that's for Park Si. And for part B, they have. Why increases by fourth clean 0.6 on average core an increase in one unit off recruiter score. So that's how we interpret the two coefficients for Part A and part B on Part C. We're asked that the school has a recruitment assessment score or 4.1. So a recruiter score is 4.1, and our traditional face is 43,000 Solution 1000 and were asked to predict the starting salary and bonus or basically asked to predict why given X one and X troops. So let's substitute that into our equation here and find the answer. So, after substituting the values, so for tuition, we would basically substitute 43 in the equation. So we get. Why is he goes toe 119 point 55 or approximately 120 1000 dollars in cellar. So these air answers from part A through T.

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