Homework #3 Answers - 1 a there is a positive linear...

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1. a. there is a positive linear association between col05 and col06, from the best fit line, it looks like about a 1 to 1 ratio. 40 60 80 100 120 60 80 100 120 COL05 COL06 b. 1. there are no obvious outliers 2. Straight enough? This plot looks straight enough to not be mistaken for a curved function, (quad, ln) so it looks straight enough to be linear 3. there are three points at the very end that very the spread at the very end of the plot, but overall the spread around the line looks about the same throughout the plot c. all: lm(formula = COL06 ~ COL05, data = CostLive) Residuals: Min 1Q Median 3Q Max -10.930 -3.482 -0.940 2.442 16.690 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 15.67986 2.28763 6.854 2.02e-10 *** COL05 0.79025 0.02808 28.145 < 2e-16 *** ---
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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 5.253 on 142 degrees of freedom Multiple R-Squared: 0.848, Adjusted R-squared: 0.8469 F-statistic: 792.1 on 1 and 142 DF, p-value: < 2.2e-16 Col06= 15.67 + .79025Col05 d. CostLive2=lm(COL06~COL05,data=CostLive) CostLive2$residuals the highest – 16.689 Sao Paulo Brazil the lowest - HARARE Zimbabwe -10.930233870 2. a. no, this graph looks logarithmic and there are too many outliers if this were a linear regression. 0 100 200 300 400 500 88 90 92 94 96 98 Bottle.Price Parker.Score b. attach(Parker) (plot(Parker.Score,Bottle.Price^.1,data=Parker))
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88 90 92 94 96 98 1.3 1.4 1.5 1.6 1.7 1.8 Parker.Score Bottle.Price^0.1 c. lmParker=lm(Bottle.Price~Parker.Score,data=Parker) boxcox(lmParker)
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-2 -1 0 1 2 -850 -800 -750 -700 -650 λ log-Likelihood 95% This shows that the function is logarithmic because the lamda value maximizes at zero. d. Bottle Price^.1 = 1.84 (from estimated graph), 1.84^10 = Bottle Price $444.8 3. a. with outlier 5 10 15 20 25 65 70 75 80 var1 var2
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Without = 1.5 2.0 2.5 3.0 3.5 4.0 4.5 65 70 75 80 Births.woman Life.Exp. The plot does not make any sense unless the outlier is not there. There is negative association between the number of children a mother has and her life expectancy b. yes in Costa Rica the average life expectancy for women is 79 and the average number of children a women may have is 25. While it may be possible that women in Costa Rica have on an average 25 children, I think that this may be a mistake.
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