Nov 1 2001 ECON 240A 1 Midterm L Phillips Answer all five questions 1 15 points All printed circuit boards PCBs that are manufactured at a certain plant are inspected for flaws Experience has shown that 50 of the PCBs produced are flawed in some way Of the flawed PCBs 60 are repairable while the remainder are seriously flawed and must be discarded A newly manufactured PCB is selected before undergoing inspection What is the probability that it will not have to be discarded 2 15 points Mensa is an organization where members possess IQ s in the top 2 of the population a If IQ s are normally distributed with a mean of 100 and a standard deviation of 16 what is the minimum IQ necessary for admission b If three individuals are chosen at random from the general population what is the probability that all three satisfy the minimum requirement for admission to Mensa 3 15 points Determine the sample size needed to estimate a sample proportion with a 95 confidence interval for its expected value of plus or minus 0 03 given a a sample proportion on the order of 0 05 b a sample proportion on the order of 0 5 c What distribution did you use in your calculations 4 15 points The following graph 4 1 shows the results of regressing California General Fund expenditures in billions of nominal dollars against California Personal Income in billions of nominal dollars beginning in fiscal year1968 69 and ending in fiscal year 2001 02 a How much of the variance in the dependent variable is explained by personal income b Interpret the estimated slope Table 4 1 follows with the estimated parameters and table of analysis of variance c Is the slope significantly different from zero What statistic do you use to answer this question What distribution do you use to answer this question What probability were you willing to accept for a Type I error Nov 1 2001 ECON 240A 2 Midterm L Phillips d What is the ratio of the explained mean square to the unexplained mean square Calfifornia General Fund Expenditures Vs California Personal Income Billions of Nominal 90 80 Gen Fund Expenditures 70 60 50 y 0 066x 1 1974 R2 0 981 40 30 20 10 0 0 200 400 600 800 1000 1200 1400 Personal Income Figure 4 1 California General Fund Expenditures Versus California Personal Income both in Billions of Nominal Dollars Table 4 1 Summary Output Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0 9904673 0 9810255 0 9804325 2 9988336 34 ANOVA df Regression Residual Total Intercept X Variable 1 SS 1 32 33 MS F Significance F 14878 68965 14878 69 1654 47398 3 98668E 29 287 7761003 8 993003 15166 46575 Coefficient Standard Error t Stat P value Lower 95 Upper 95 s 1 197411 0 927956018 1 29037 0 20616709 3 08759378 0 6927721 0 0659894 0 001622349 40 67523 3 9867E 29 0 062684796 0 069294 Nov 1 2001 ECON 240A 3 Midterm L Phillips 5 15 points The following graph 5 1 shows the results of regressing the logarithm of California General Fund Expenditures in billions of nominal dollars against the logarithm of California Personal Income in billions of nominal dollars a How much of the variance in the dependent variable is explained by the independent variable b Interpret the estimated slope c Express the fitted equation in terms of the variables California General Fund Expenditures fitted and California Personal Income The Logarithm of California General Fund Expenditures Vs The Logarithm of California Personal Income Billions of Nominal Dollars CA Gen Fund Expenditures 100 y 0 0398x1 0737 R2 0 9877 10 1 10 100 1000 CA Personal Income Figure 5 1 The Logarithm of California General Fund Expenditures Versus the logarithm of California Personal Income both in Billions of Nominal Dollars Table 5 1 follows with the estimated parameters d Test the hypothesis that the slope equals one e What is the economic political significance of this hypothesis test 10000 Nov 1 2001 ECON 240A 4 Midterm L Phillips Table 5 1 Variable LNPERSINC C R squared Adjusted R squared S E of regression Coefficient 1 073723 3 224482 0 987708 0 987324 0 100384 Std Error 0 021175 0 125736 Mean S D Akaike Sum squared resid Log likelihood Durbin Watson stat 0 322461 30 94437 0 347529 Schwarz F statistic Prob F t Statistic 50 70825 25 64487 Prob 0 0000 0 0000 3 091322 0 891602 1 702610 1 612824 2571 327 0 000000 Figure5 2 follows Figure 5 2 Plot of Actual Fitted and Residuals for the Logarithm of California General Fund Expenditures Regressed on the Logarithm of California Personal Income 5 4 3 0 3 0 2 2 0 1 1 0 0 0 1 0 2 70 75 80 Residual 85 90 Actual 95 00 Fitted f Is there any evidence of multicollinearity Why or why not g Is there any evidence of autocorrelation Why or why not
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