(a) Based on the F test of overall signicance and the coefficient of determination, do you think this model would be useful in predicting the obesity rate of a country? Explain your answer. (b) Do the slope estimates have the signs you would expect? Why or why not? Develop and test appropriate hypotheses concerning the slope coefcients using 1'- tests at the 5% significance level. What do you conclude? (c) Carefully explain the meanings of the estimated slope coefficients. Does the y- intercept estimate have a logical interpretation? Why or why not? If it does, how do you interpret it? (d) Does it appear that the normality requirement is satisfied? Why or why not? Use as much information as you can form the R printouts and be specific. What does this imply about the reliability of the F and ttests? (e) Does the homoskedasticity assumption seem to be satisfied? Why or why not? Use as much information from the R printouts as you can and be specific. (f) Compare the ttests on the slope parameters based on the usual and on the heteroskedasticity consistent standard errors. What do these comparisons suggest about the practical implications of heteroskedasticity this time? "(30 marks: 5+4+8+6+4+3) A hot topic lately is the economic effect of obesity. A researcher studying the obesity rate (OR, %), the proportion of obese people in the adult population, in various countries hypothesizes that it is a function of the number of McDonald's restaurants per 1,000 people (MD) and the number of television per 1,000 people (TV). He collects data on these three variables from 28 OECD countries and generates the following R printouts. On these printouts res is the OLS residual and OR_hat is the estimate of OR. Your job is to evaluate the researcher's results. OR MD TV Call: median 12 . 800 0. 130 466. 373 1m(formula = OR ~ MD + TV) mean 13 . 854 0. 156 464. 933 Residuals : SE . mean 1. 220 0. 021 25 .079 Min 1Q Median 3Q Max CI . mean . 0. 95 2 . 504 0. 044 51 . 459 -10 . 805 -3.539 -1. 022 2. 524 12.956 var 41 . 697 0. 013 17611 . 314 Coefficients : std . dev 6. 457 0. 113 132 . 708 Estimate Std. Error t value Pr(>|t|) coef. var 0 . 466 0. 723 0. 285 (Intercept) 17 .26688 4. 59623 3.757 0. 000923 * * * MD 31. 39248 14. 33512 2. 190 0. 038076 * skewness 0 . 628 0. 917 0. 087 TV -0. 01785 0. 01216 -1. 468 0. 154552 skew . 2SE 0. 712 1. 040 0. 099 Signif. codes: 0 '* **' 0.001 '* * ' 0.01 ' *' 0.05 '. ' 0.1 ' ' 1 kurtosis -0. 137 -0. 189 -0. 866 kurt . 2SE -0. 080 -0.110 -0. 505 Residual standard error: 6.147 on 25 degrees of freedom Multiple R-squared: 0.161, Adjusted R-squared: 0. 09385 normtest . W 0. 941 0. 893 0. 971 F-statistic: 2.398 on 2 and 25 DF, p-value: 0. 1115 normtest . p 0. 117 0. 008 0. 611res Histogram of res median -1. 02200e+00 mean 0. 00000e+00 SE . mean 1. 11800e+00 CI . mean . 0. 95 2. 29400e+00 0.10 var 3. 49850e+01 std . dev 5. 91500e+00 coef. var 8. 78287e+16 0.08 skewness 3.91000e-01 skew. 2SE 4. 44000e-01 kurtosis -5. 14000e-01 0.06 kurt . 2SE -2 . 99000e-01 normtest . W 9. 63000e-01 Density normtest . p 4. 00000e-01 0.04 0.02 0.00 Normal Q-Q plot of res 15 -10 -5 0 5 10 15 res . . . OLS residuals versus OR_hat LO Sample quantiles TO res O -2 -1 0 1 2 10 12 14 16 18 20 Theoretical quantiles OR_hatstudentized Breusch-Pagan test data: m BP = 13.608, df = 5, p-value = 0. 0183 t test of coefficients based on HC standard errors: Estimate Std. Error t value Pr(>|t|) (Intercept) 17.266878 5. 056277 3.4149 0. 002184 * * MD 31 . 392476 11 . 298437 2.7785 0. 010212 TV -0. 017846 0. 010959 -1. 6284 0. 115981