252x0644 12/14/05 ECO252 QBA2Final EXAMDecember , 2006Version 4Name and Class hour:_________________________I. (18+ points) Do all the following. Note that answers without reasons and citation of appropriate statistical tests receive no credit. Most answers require a statistical test, that is, stating or implying a hypothesis and showing why it is true or false by citing a table value or a p-value. If you haven’t done it lately, take a fast look at ECO 252 - Things That You Should Never Do on a Statistics Exam (or AnywhereElse)Regression B seeks to explain the selling price of a home in terms of a group of variables explained on theoutput sheet. Note that regressions 12 and 17 are identical. Look at the definitions of the variables carefully and, in particular, notice which are interaction variables.a) The homes in this regression have been rated High, Med or Low by realtors. There are dummy variables to indicate the ratings. Why didn’t I use High or AH in regression 12? (1)b) In Regression 12, what coefficients are significant at the 1% level? (2)c) What independent variables did I remove from the problem to get to Regression 13 from Regression 12?Why? (2)d) Following the same process, I went on to remove one or more variables to get to Regression 13. When Igot to Regression 13 I ran the ‘best subsets regression.’ 14. I concluded that it was time to quit removing variables. Between the best subsets regression and the characteristics of the coefficients of the results in Regression 13 I felt that I had gone as far as was reasonable in removing independent variables. What are the three things that led me to think that regression 5 was almost the best that I could do? Remember that a close relationship between Sq.ft and Sqftsq is excusable. What in the printout might make you question my judgment? (3)e) Using Regression 13 and assuming that all homes have areas of 1000 sq ft., Regression 13 effectively becomes 3 regressions relating Market price to Assessment. Take the coefficient of Sq.ft, multiplied by 1000 and the coefficient of Sqftsqsq multiplied by 21000. Add them to the constant to get the effective intercept for homes with areas of 1000 sq. ft.. Using A or any other symbol that you find convenient forliving area, what are the equations relating assessment to Market price for (4 points)Low homes?Med homes?High homes ?Is the difference between the slopes of these three equations relative to market significant? Why? [12]f) Continuing with Regression 13 and assuming that a home has 1000 square feet of living area and an assessment of 24, what would it sell for if it were ratedLow?1252x0644 12/14/05 Med?High?What is the percent difference between the lowest and highest price? (2)g) We have not yet dealt with the question of whether the coefficients in Regression 5 are reasonable. In order to do this look at two homes, one with an area of 1000 and the second with an area of 1001. By how much will their Market prices differ? Does that seem reasonable? (3) [17]h) As I warned you, I now repeated Regression 12 as Regression 15, without using the VIFs. I decided to drop 1 variable. Why? (1)i) I could now add AH to the independent variables and did equation 16. I dropped it immediately. Why? (1)j) I now ran Regression 17 without one fewer independent variable than Regression 15 and did the same thing to get to Regression 18. How does Regression 18 compare with Regression 13? (2) j) Regression 17 is a stepwise regression. The printout presents four different possible regressions in column form. Look at in each case a coefficient has a t-value under it and a p-value for a significance test. After the fourth try, the computer refused to add any more independent variables. The only regression herethat I thought was worth looking at was the one with four independent variables. What can you tell me about its acceptability? (3) [24]k) Do an F test to compare regressions 15 and 18 and to see if the two variables removed had any explanatory power.II. Hand in your third computer problem. (2 to 7 points) 2252x0644 12/14/05 III. Do at least 4 of the following 7 Problems (at least 12 each) (or do sections adding to at least 50 points – (Anything extra you do helps, and grades wrap around). You must do parts a) and b) of problem 1. Show your work! State H0 and H1where applicable. Use a significance level of 5% unless noted otherwise. Do not answer questions without citing appropriate statistical tests – That is, explain your hypotheses and what values from what table were used to test them. Clearly label what section of each problem you are doing! The entire test has about 151 points, but 70 is considered a perfect score. Don’t waste our time by telling me that two means, proportions, variances or medians don’t look the same to you. You need statistical tests! There are two blank pages below.1. a) If I want to test to see if the mean of 2x is smaller than the mean of 1x my null hypotheses are: (Note: 21D)i) 21 and 0Dii) 21 and 0Diii) 21 and 0Div) 21 and 0Dv) 21 and 0Dvi) 21 and 0Dvii) 21 and 0Dviii) 21 and 0D (2) The first two columns below represent times for 25 workers on an industrial task. The third column is the difference between themRow 1x 2x d 1 5.11 4.81 0.30 2 4.13 4.19 -0.06 3 5.42 5.17 0.25 4 3.65 4.07 -0.42 5 4.82 4.58 0.24 6 3.08 2.97 0.11 7 3.01 3.39 -0.38 8 4.26 4.14 0.12 9 4.25 4.31 -0.06 10 6.66 6.68 -0.02 11 5.29 5.37 -0.08 12 4.41 3.95 0.46 13 5.17 4.93 0.24 14 4.50 4.04 0.46 15 3.06 2.40 0.66 16 5.19 4.71 0.48 17 5.71 5.93 -0.22 18 3.41 2.93 0.48 19 4.25 4.25 0.00 20 3.85 4.41 -0.56 21 5.50 4.68 0.82 22 4.24 3.50 0.74 23 6.29 6.09 0.20 24 3.99 2.87 1.12 25 3.26 3.06 0.20Assume that 05.. Minitab gives us the following summary (edited).Descriptive Statistics: x1, x2, d Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximumx1 25 0 4.50 0.200 1.001 3.010 3.750 4.260 5.240 6.660x2 25 0 4.30 0.212 1.062 2.400 3.445 4.250 4.870 6.680d 25 0 0.20 …………… …………… -0.5600 -0.0600 0.2000 0.4700 1.1200In the d column, the column sum is 5.08 and the sum of the first 24 numbers squared is 4.825. Do not recompute things that have been done for you if you want to ever get much done on this exam. Clearly label parts b, c, d etc.
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