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Cal Poly STAT 252 - Exam 3

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Name ___________________________ Stat 252 Summer 2001 Exam 31. In the output that follows, the response is the price of compact cameras. The independent variables are the weight in ounces (x1), image quality on a scale of 1 to 10 (x2), and flash range in feet (x3).The regression equation isy = - 265 + 42.3 x1 + 25.4 x2 - 7.91 x3Predictor Coef SE Coef T PConstant -264.8 198.3 -1.34 0.202x1 42.33 12.25 3.46 0.004x2 25.35 23.77 1.07 0.303x3 -7.908 8.013 -0.99 0.339S = 70.92 R-Sq = 57.2% R-Sq(adj) = 48.6%Analysis of VarianceSource DF SS MS F PRegression 3 100724 33575 6.68 0.004Residual Error 15 75444 5030Total 18 176168The regression equation isy = - 72.9 + 33.9 x1Predictor Coef SE Coef T PConstant -72.90 67.65 -1.08 0.296x1 33.907 7.803 4.35 0.000S = 70.07 R-Sq = 52.6% R-Sq(adj) = 49.8%Analysis of VarianceSource DF SS MS F PRegression 1 92699 92699 18.88 0.000Residual Error 17 83469 4910Total 18 176168The regression equation isy = - 30 + 11.2 x2 + 13.1 x3Predictor Coef SE Coef T PConstant -29.8 241.7 -0.12 0.904x2 11.17 30.38 0.37 0.718x3 13.147 6.755 1.95 0.069S = 92.03 R-Sq = 23.1% R-Sq(adj) = 13.5%Analysis of VarianceSource DF SS MS F PRegression 2 40645 20323 2.40 0.123Residual Error 16 135523 8470Total 18 176168A claim has been made that a model with X1 alone is sufficient to predict price, rather than a model thatincludes all three independent variables under consideration. Test this hypothesis at a level of significance of 0.05.a) What are the hypotheses? (3)b) What is the decision rule? (3)c) Calculate the value of the test statistic. (4)d) Reach a decision and provide an interpretation of the result. (4)e) Does this result tell you what the final model should be? Explain.2. A banker is interested in predicting mortgage rates (Y) based on national housing sales (X1) and the season of the year (winter, spring, summer, fall). a) Write an appropriate model and define the dummy variables that would allow for differences between the four seasons of the year, but would restrict the change in mortgage rates for an increase in housing sales (i.e., the slope) to be the same for all four seasons of the year. (3)b) Give the mean mortgage rate for each season of the year using this model, i.e., write winter, spring, summer, and fall, in terms of the model. (3)c) Indicate the test (t, global-F, partial-F) that could be used to see if housing sales and/or the season of the year are related to mortgage rates in this model. (Note: Answer partial-F only if it is the only way to perform the test.) (2)d) Indicate the test (t, global-F, partial-F) that could be used to see if there is any difference in the average interest rate for the four seasons of the year in this model. (Note: Answer partial-F only ifit is the only way to perform the test.) (2)e) Indicate the test (t, global-F, partial-F) that could be used to see if there is a relation between housing sales and the average interest rate in this model. (Note: Answer partial-F only if it is the only way to perform the test.) (2)f) Write an appropriate model which would allow for four different linear relations to exist between mortgage rates and housing sales in each part of the country (i.e., allows for both different intercepts and different slopes). (3)3. An economist believes that the relation between GNP (Y) and the production of heavy machinery (X1) and trade balance (X2) is of the form: Y =    21210XX. a) This relation is described as being intrinsically linear. What does this mean? (2)b) Explain how you would use a package such as MINITAB to fit this model:i) What dependent and independent variables would you regress? (2)ii) What would b0, b1, and b2 estimate? (2)iii) Once the model is fit, how would you use it to estimate the value of Y for any particular combination of (X1) and (X2)? (2)4. The MINITAB output that follows includes several variable selection procedures used to select reasonable models to predict a response, y, from a set of 11 potential predictors. Answer all parts of this question with specific regard to the MINITAB output.a) Examining the backwards stepwise output, how many and what type(s) of model(s) (e.g., 1 MLR model with all 7 variables, 5 SLR models, 9 MLR models with 3 x's, two of which are x2 and x4) is(are) used on the first step? (2)b) Examining the backward stepwise output, which was the first variable removed from the model, and why was it selected for removal? (2)c) Why did the backward stepwise process cease when it did? (2)d) Examining the forward stepwise output, how many and what type(s) of model(s) is (are) used on the first step? (2)e) Examining the general stepwise output, which was the first variable entered into the model, and why was it selected for inclusion? (2)f) Examining the forward stepwise output, how many and what type(s) of model(s) is (are) used on the second step? (2)g) There was a fifth step in the forward stepwise procedure for which no output was printed. How many and what type(s) of model(s) is (are) used on that step? (2)h) Why did the forward stepwise process cease when it did, i.e., describe what the stepwise program evaluated on the fifth step for which there is no output. (2)i) Explain how the general stepwise procedure differs from the forward stepwise procedure. (2)j) Each of the three procedures yielded a different estimated model. Given that the data values of thepredictors are readily available, which appears to be the best model of the three? (2)k) How and why do the results of the “best reg” procedure differ from those of the various stepwise procedures? (2)l) Given the “best reg” procedure output, discuss what model or models you would consider and explain your reasoning. (2)Backward elimination.


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Cal Poly STAT 252 - Exam 3

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