2. Suppose that QED, Inc. estimates weekly demand for good X, Qx, and obtains the parameter estimates below from a multiple regression using the double-log model: Px Py Pz I Intercept 3.402 Coefficients -2.2 1.8 -0.55 -0.8 t-statistics 4.12 2.73 2.09 -7.54 where Px = price of good X, Py = price of good Y, Pz = price of good Z, and I = monthly per capita personal income. Also, multiple R² = 0.86, n = 20, and F-statistic = 17.08. a) Using the above results, construct (write out) the estimated regression equation (i) in the double log form, and, (ii) in the power or multiplicative function form. b) Interpret and explain the coefficients of Py, P₂, and I. c) Assuming a 5% significance level (k = 0.05), determine the degrees of freedom and the critical t-value. Perform t-tests on the parameter estimates for Py and P₂. Clearly and explicitly state the hypotheses for each parameter that you are testing. d) Assuming a 5% significance level (k = 0.05), perform an F-test on the entire regression. Clearly and explicitly state the hypothesis that you are testing. e) Explain the meaning of the multiple R². Briefly discuss the robustness of the estimated model, i.e., how "good" is it?

2. Suppose that QED, Inc. estimates weekly demand for good X, Qx, and obtains the parameter estimates below from a multiple regression using the double-log model: Px Py Pz I Intercept 3.402 Coefficients -2.2 1.8 -0.55 -0.8 t-statistics 4.12 2.73 2.09 -7.54 where Px = price of good X, Py = price of good Y, Pz = price of good Z, and I = monthly per capita personal income. Also, multiple R² = 0.86, n = 20, and F-statistic = 17.08. a) Using the above results, construct (write out) the estimated regression equation (i) in the double log form, and, (ii) in the power or multiplicative function form. b) Interpret and explain the coefficients of Py, P₂, and I. c) Assuming a 5% significance level (k = 0.05), determine the degrees of freedom and the critical t-value. Perform t-tests on the parameter estimates for Py and P₂. Clearly and explicitly state the hypotheses for each parameter that you are testing. d) Assuming a 5% significance level (k = 0.05), perform an F-test on the entire regression. Clearly and explicitly state the hypothesis that you are testing. e) Explain the meaning of the multiple R². Briefly discuss the robustness of the estimated model, i.e., how "good" is it?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
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