QUESTION 1: Function Form regression Model Using the Comb Douglas production function for API generation, the empirical results are given as follows: Model X : Y = 12.4281-0.7608pl -24.6154pk-12.3621pf (15.8223) (3.2471) (24.1574) (4.5137) Adjusted R-square = 0.7999
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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?The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
- 10.1 You estimated a regression with the following output. Source | SS df MS Number of obs = 213 -------------+---------------------------------- F(1, 211) = 4905.10 Model | 112084380 1 112084380 Prob > F = 0.0000 Residual | 4821474.15 211 22850.5884 R-squared = 0.9588 -------------+---------------------------------- Adj R-squared = 0.9586 Total | 116905854 212 551442.706 Root MSE = 151.16 ------------------------------------------------------------------------------ Y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- X | 25.44706 .3633405 70.04 0.000 24.73082 26.16331 _cons | 68.53346 32.19625 2.13 0.034 5.065942 132.001…Refer to the following computer output from estimating the parameters of the nonlinear model Y = aRbScTd The computer output from the regression analysis is: DEPENDENT VARIABLE: LNY R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT -0.6931 0.32 -2.17 0.0390 LNR 4.66 1.36 3.43 0.0019 LNS -0.44 0.24 -1.83 0.0774 LNT 8.28 4.60 1.80 0.0826 Based on the information in the table, which of the parameter estimates are statistically significant at the 90% level of confidence?Refer to the following computer output from estimating the parameters of the nonlinear model Y = aRbScTd The computer output from the regression analysis is: DEPENDENT VARIABLE: LNY R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT -0.6931 0.32 -2.17 0.0390 LNR 4.66 1.36 3.43 0.0019 LNS -0.44 0.24 -1.83 0.0774 LNT 8.28 4.60 1.80 0.0826 Based on the information in the table, if R = 1, S = 2, and T = 3, what value do you expect Y will have?
- Refer to the following computer output from estimating the parameters of the nonlinear model Y = aRbScTd The computer output from the regression analysis is: DEPENDENT VARIABLE: LNY R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT -0.6931 0.32 -2.17 0.0390 LNR 4.66 1.36 3.43 0.0019 LNS -0.44 0.24 -1.83 0.0774 LNT 8.28 4.60 1.80 0.0826 Based on the information in the table, if S increases by 8% (all other things constant), Y will MultipleAlthough the Excel regression output, shown in Figure 12.21 for Demonstration Problem 12.1, is somewhat different from the Minitab output, the same essential regression features are present. The regression equation is found under Coefficients at the bottom of ANOVA. The slope or coefficient of x is 2.2315 and the y-intercept is 30.9125. The standard error of the estimate for the hospital problem is given as the fourth statistic under Regression Statistics at the top of the output, Standard Error = 15.6491. The r2 value is given as 0.886 on the second line. The t test for the slope is found under t Stat near the bottom of the ANOVA section on the “Number of Beds” (x variable) row, t = 8.83. Adjacent to the t Stat is the p-value, which is the probability of the t statistic occurring by chance if the null hypothesis is true. For this slope, the probability shown is 0.000005. The ANOVA table is in the middle of the output with the F value having the same probability as the t statistic,…Just parts d,e anf f of question 1 d) We conduct a simple regression of size on hhinc, now using robust standard errors. The regression output is reported in Table 2. Why are the estimated coefficients in Table 2 equal to the estimated coefficients in Table 1? Do the conclusions on the statistical significance at 5% of the coefficient of hhinc change between Tables 1 and 2? e) Now, using both the critical value and the p-value, test whether the coefficient of hhinc is statistically significant at 1%, by using the results in Table 1. Repeat the test by using the results in Table 2. Compare the results based on Table 1 with the results based on Table 2. Consider the results in Table 2. Compute the 99% confidence interval for hhinc. f) Consider the results in Table 2.How would you decide whether 0 is contained in the 99% confidence interval for the coefficient of hhinc, without actually computing the confidence interval?
- ch 11. 4 Oxnard Petro, Ltd., has three interdisciplinary project development teams that function on an ongoing basis. Team members rotate from time to time. Every 4 months (three times a year) each department head rates the performance of each project team (using a 0 to 100 scale, where 100 is the best rating). Are the main effects significant? Is there an interaction?Consider the following regression model: Dependent Variable: MU Sample: 134 Variable b BETA t-Statistic P-value Constant 7.292206 6.666348 0.0000 COLLEGE -0.115133 -0.23 -4.437697 0.0000 GROWTH 0.018898 0.01 1.718810 0.0880 SENIORS -0.022380 -0.24 -0.731017 0.4661 WAGE -0.0000294 -0.001 -0.874836 0.3833 R-squared 0.192456 Mean dependent var 3.852239 Adjusted R-squared 0.167416 S.D. dependent var 1.928368 Where MU = metropolitan area unemployment rate, COLLEGE = percentage of the metropolitan area population with a college degree, GROWTH = growth rate of the metropolitan area population, SENIORS = percentage of the metropolitan area population that is elderly, and WAGE = average metropolitan area wage Which two variables have the least impact on MU?Question 2: The estimated regression equation for a model involving two independent variables and 65 observations is: yhat = 55.17+1.1X1 -0.153X2 Other statistics produced for analysis include: SSR = 12370.8, SST = 35963.0, Sb1 = 0.33, Sb2 = 0.20.a. Interpret b1 and b2 in this estimated regression equation b. Predict y when X1 = 65 and X2 = 70. c. Compute R-square and Adjusted R-Square. d. Comment on the goodness of fit of the model. e. Compute MSR and MSE. f. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05). g. Perform a t test using the critical value approach for the significance of β1.Use a level of significance of 0.05. h. Perform a t test using the critical value approach for the significance of β2.Use a level of significance of 0.05.