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02 STAT descriptive statistics 3-IC Q2 Q3

02 STAT descriptive statistics 3-IC Q2 Q3 - Dr V.R...

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Unformatted text preview: Dr. V.R. Bencivenga Economics 329 Economic Statistics DESCRIPTIVE STATISTICS 3—INDEX CARD QUESTIONS 2 AND 3 IC Q 2 MBA tuition and starting salaries. Business schools that train MBA’s vary a great deal in the tuition they charge. As one would expect, starting salaries also vary substantially across MBA programs. Is there a relationship between the two? Let’s investigate, using Business Week data for 50 business schools. These data are from an on-line article, “Return on Investment,” March 7, 2007. If you are interested, the article is available at: http://www.businessweek.com/magazine/content/07_12/b4026072.htm. The data are available on Blackboard as an Excel file: MBA salary relative to tuition BUS WK.xls. The article ranks 29 private schools and 21 public schools (separately) according to the ratio of median starting salary to tuition. The relationship we are interested in can be expressed as a regression model: SALARYi 0 1TUITIONi ui where SALARYi = median starting salary of MBA’s graduating from school i TUITIONi = annual tuition charged by school i The results of estimating the model on observations on private schools are: SALARY = 43610 + 0.207 TUITION The results of estimating the model on observations on public schools are: SALARY = 45039 + 0.327 TUITION The results of estimating the model on the entire sample of 50 schools are: SALARY = 46481 + 0.118 TUITION a. ˆ Interpret 1 for public schools. Is this value consistent with the hypothesis that a more expensive MBA is expected to result in a higher starting salary? Explain. According to these estimated relationships, does an additional dollar of tuition increase predicted starting salary more for an MBA at a public school or a private school? (Hint: Resources to help you with this are the lecture slides and the beginning of Ch 11. Example 11.2 on pg. 430 is a good example to follow.) b. ˆ Are you surprised at the value of 1 for the entire sample of 50 schools? Can you think of ˆ an explanation for why 1 is smaller for the entire sample than it is for public schools or private schools separately? c. These samples were chosen by Business Week on the basis of the ratio of starting salary to tuition (large values of the ratio were chosen). Is there any selection issue here that ˆ might bias 1 (compared to if we had data from a random sample of business schools)? IC Q 3 You have data on two variables, X and Y. Consider the following two models: Yi 0 1 X i ui X i 0 1 Yi v i I.e., one model regresses Y on X, and the other regresses X on Y. Both are estimated with least 1 ˆ 1 if and only if rXY 1 or rXY 1 (i.e., if and only if the squares. Show that ˆ 1 observations on X and Y lie exactly on a straight line)! Note: Answering this question will give you a lot of intuition about correlation—in particular, it will show you why 1 rXY 1 ! ...
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