Oct 25 2007 Due Nov 1 2007 ECON 140A 240A 1 Problems 4 L Phillips 1 The densities in Figure 1 are from the normal and Student s t They can be interpreted as 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 Figure 1 Densities 0 5 0 4 0 3 DENSA DENSB DENSC 0 2 0 1 0 0 4 2 0 2 4 Y 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 Oct 25 2007 Due Nov 1 2007 ECON 140A 240A 2 Problems 4 L Phillips c 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 fit f Do you see any of the assumptions of ordinary least squares violated Explain Table 2 Dependent Variable LNCAINC Method Least Squares Sample 1968 2000 Included observations 33 Variable Coefficient Std Error t Statistic Prob C YEAR 156 5537 0 081845 4 817282 0 002428 32 49835 33 70834 0 0000 0 0000 R squared Adjusted R squared S E of regression Sum squared resid Log likelihood Durbin Watson stat 0 973442 0 972585 0 132812 0 546807 20 82778 0 053283 Mean dependent var S D dependent var Akaike info criterion Schwarz criterion F statistic Prob F statistic 5 826964 0 802128 1 141078 1 050380 1136 252 0 000000 Figure 2 Actual Fitted and Residual from Regressing the Logarithm of CA Personal Income Against Year 8 7 6 5 0 2 4 0 1 0 0 0 1 0 2 0 3 70 75 80 Residual 85 Actual 90 95 Fitted 00 Oct 25 2007 Due Nov 1 2007 ECON 140A 240A 3 Problems 4 L Phillips 3 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 crosscountry a What percentage of these university students ski both downhill and cross country b What percentage of the university students do not ski at all
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