Stat Pset 9 - 80 100 Bill 120 140 160 Stat Pset 9 Melissa...

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Stat Pset 9 November 18, 2015 Melissa Kaplan 1. From inspection the variables look they have a relationship, which can be approximated by some sort of parabolic function. -.48 is the slope, which means for every increase in degree of temperature the monthly bill will decrease by $.48 R 2 =.12. %12 of the variation in the monthly bill can be explained by the variation in temperature. T=-1.19, so we fail to reject the null hypothesis... Not enough evidence to say B 1 is not equal to 0. So there may be no linear correlation. This makes sense as the shape looks parabolic not linear. 0 is in the confidence interval so this is reasonable that we do not reject the null hypothesis. 80 100 120 140 160 Bill 40 50 60 70 80 90 Temp _cons 143.6228 25.99548 5.52 0.000 85.70126 201.5444 temp -.4798844 .4032247 -1.19 0.261 -1.378325 .4185561 bill Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 6263.25 11 569.386364 Root MSE = 23.423 Adj R-squared = 0.0365 Residual 5486.19715 10 548.619715 R-squared = 0.1241 Model 777.052845 1 777.052845 Prob > F = 0.2615 F(1, 10) = 1.42 Source SS df MS Number of obs = 12 . regress bill temp
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If Bill=120, than temperature is 49.17. This answer is unreasonable, as it could be 49 or it could also be 85 according to the data… this linear regression does not fit the function. Confidence Interval: average +/- root MSE*1.96= 114.8 ± 45.91= (68.89,160.71) 2. question 2 The variables look to have a positive linear correlation. Height= 11.76 (stories) +102.42 An extra story adds 11.76 feet to a building. T=8.06>1.96 so we reject the null hypothesis that the slope is 0. So these variables do have a linear correlation. 0 is not in the confidence interval so we can reject the null hypothesis.
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