Oct. 20, 2005 ECON 240A-1 L. PhillipsDue Oct. 27, 2005 Problems #41. The densities in Figure 1 are from the normal and Student’s t. They can be interpretedas representing a sequence of distributions depending on a parameter characterizing samples.a.Label the densities as normal or Student’s t.b. Which changing sample parameter is causing a movement from one density to another?c.Label each density one, two, or three for its position in the sequence, and explain the connection between your answer to part c and your answer to part b.d. Is it possible that all of the densities in Figure 1 are Student’s t? Explain.2. The logarithm of California personal income, LNCAINC, in billions of current or nominal dollars, was regressed against year, from 1968 through 2000, where 1968 is fiscal year 1968-1969. The results are shown in Table 2. A plot of actual, fitted, and residual follows. a.How should the slope parameter be interpreted in this regression?b. Is it significantly different from zero? Describe the null hypothesis, the alternative hypothesis, and the statistic you use to test the null hypothesis. 0.00.10.20.30.40.5-4 -2 0 2 4YDENSADENSBDENSCFigure 1: DensitiesOct. 20, 2005 ECON 240A-2 L. PhillipsDue Oct. 27, 2005 Problems #4c.If California Personal Income was $1028 billion in fiscal year 2000-2001, what value would you predict for fiscal year 2001-2002?d. What kind of growth curve for California personal income is being estimated using the regression of the natural logarithm of personal income against year?e.Comment on the goodness of fitf. Do you see any of the assumptions of ordinary least squares violated? Explain.------------------------------------------------------------------------------------Table 2Dependent Variable: LNCAINCMethod: Least SquaresSample: 1968 2000Included observations: 33Variable Coefficient Std. Error t-Statistic Prob. C -156.5537 4.817282 -32.49835 0.0000YEAR 0.081845 0.002428 33.70834 0.0000R-squared 0.973442 Mean dependent var 5.826964Adjusted R-squared 0.972585 S.D. dependent var 0.802128S.E. of regression 0.132812 Akaike info criterion -1.141078Sum squared resid 0.546807 Schwarz criterion -1.050380Log likelihood 20.82778 F-statistic 1136.252Durbin-Watson stat 0.053283 Prob(F-statistic) 0.000000----------------------------------------------------------------------------------------0.3-0.2-0.10.00.10.24567870 75 80 85 90 95 00Residual Actual FittedFigure 2: Actual Fitted and Residual from Regressingthe Logarithm of CA Personal Income Against YearOct. 20, 2005 ECON 240A-3 L. PhillipsDue Oct. 27, 2005 Problems #43. A sporting goods store estimates that 20% of the students at a nearby university ski downhill and 15% ski cross-country. Of those who ski downhill, 40% also ski cross-country.a.What percentage of these university students ski both downhill and cross-country?b. What percentage of the university students do not ski at
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