252x0641 12/15/05 ECO252 QBA2Final EXAMDecember , 2006Version 1Name 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 A seeks to explain the selling price of a home in terms of a group of variables explained on the output sheet. Note that regressions 1 and 7 are identical. Look at the definitions of the variables carefully and, in particular, notice which are interaction variables.a) The homes in this regression are in three different areas. There are dummy variables to indicate that thehomes are in Area 1 or Area 2. Why isn’t there a dummy variable for Area 3? (1)b) In Regression 1, what coefficients are significant at the 5% level? (2)c) What independent variables did I remove from the problem to get to Regression 2 from Regression 1? Why? (2)d) Following the same process, I went on to remove one or more variables each time until I got to Regression 5. When I got to Regression 5 I ran the ‘best subsets regression.’ 6. 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 5 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 the best that I could do? (3)e) Using Regression 5 and assuming that all homes have two baths, Regression 5 effectively becomes 3 regressions relating price to living area. Take the coefficient of bath, multiply it by two and add it to the constant to get the effective intercept for homes with two baths. Using L or any other symbol that you find convenient for living area, what are the equations relating living area to price in (3 points)Area 1?Area 2?Area 3? [11]f) Continuing with Regression 5 and assuming that a home has 2(thousand) square feet of living area and 2 baths, what would it sell for inArea 1?Area 2?Area 3?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 in Area 1 that have two baths. If one has 2(thousand) square feet of 1252x0641 12/15/05 living area and the other 3, how would there prices differ? Does that seem reasonable? Try the same for a home in area 3. (3) [16]h) As I warned you, I now repeated Regression 1 as Regression 7, without using the VIFs. Much to my surprise, I ended up dropping the same variables as I did after Regression 1. Why? (1)i) Continuing in the same way, I worked myself to Regression 9. Looking at the things I usually check, this looked pretty good. Then I tried to check the coefficients in the same way that I did in g). Why was I very unhappy? What is there in Regression 8 that could explain these results? (4) j) Regression 11 is a stepwise regression. The printout, which continues on page 7 presents four different possible regressions in column form. Look at in each case a coefficient has a t-value under it and a p-valuefor a significance test. After the fourth try, the computer refused to add any more independent variables. The only regression here that 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 2 and 3 and to find out if lot 1 and lot 2 have any explanatory power. (3)II. Hand in your third computer problem. (2 to 7 points) 2252x0641 12/15/05 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 larger 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 6.11 4.81 1.30 2 5.13 4.19 0.94 3 6.42 5.17 1.25 4 4.65 4.07 0.58 5 5.82 4.58 1.24 6 4.08 2.97 1.11 7 4.01 3.39 0.62 8 5.26 4.14 1.12 9 5.25 4.31 0.94 10 7.66 6.68 0.98 11 6.29 5.37 0.92 12 5.41 3.95 1.46 13 6.17 4.93 1.24 14 5.50 4.04 1.46 15 4.06 2.40 1.66 16 6.19 4.71 1.48 17 6.71 5.93 0.78 18 4.41 2.93 1.48 19 5.25 4.25 1.00 20 4.85 4.41 0.44 21 6.50 4.68 1.82 22 5.24 3.50 1.74 23 7.29 6.09 1.20 24 4.99 2.87 2.12 25 4.26 3.06 1.20Assume 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 5.50 0.200 1.00 4.010 4.750 5.260 6.240 7.660x2 25 0 4.30 0.212 1.06 2.400 3.445 4.250 4.870 6.680d 25 0 1.20 ………… ……… 0.4400 0.9400 1.200 1.4700 2.120In the d column, the column sum is 30.08 and the sum of the first 24 numbers squared is 38.585. 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. The null hypothesis is the same for parts c, d and e, so state it clearly.b). Find the sample variance for the d column. (2)3252x0641 12/15/05 c) On the assumption that the underlying distributions are Normal and that
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