Data were collected on distance between a person\'s home andprimary work locatio
ID: 2949985 • Letter: D
Question
Data were collected on distance between a person's home andprimary work location (distance) and the person's monthlyexpenditures on gas (gas) for 17individuals. The data follow.
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Conduct a regression analysis to predict gas expenditure givendistance from work. For all parts of this problem, give answers totwo decimal places.
distance gas 37 195.83 24 160.86 36 186.14 17 168.93 24 151.16 13 128.67 21 141.09 11 137.29 15 139.85 11 149.69 36 172.54 11 112.69 38 190.62 24 140.06 40 211.2 26 182.24 18 140.62Explanation / Answer
a sol :- Let X is distance between a person's home and primarylocation and Y is person's monthly expenditure. Y = +X+U where is intercept and is theslope and both are constants. Yhat = hat+Xhat Using least square estimation, the residualsum of squares is minimum. so thenormal equations are Y = n + X andYX = X + X2 X Y 37 195.83 24 160.86 36 186.14 17 168.93 24 151.16 13 128.67 21 141.09 11 137.29 15 139.85 11 149.69 36 172.54 11 112.69 38 190.62 24 140.06 40 211.2 26 182.24 18 140.62 X = 402 Y =2709.48 YX = 67970.60 X2 = 11220.00 Xbar = 23.65 Ybar= 159.38 2709.48 = 17 + 402 67970.60 = 402 + 11220 = 2.28 & = 105.58 Yhat = 105.58+ 2.28X C sol :- Correlation between Gas &Distance corr(x,y) =cov(x,y)/sqrt(var(X)*var(Y)) consider, covariance of x &Y is,Cov(X,Y) = 228.93 miles Varianceof X is, var(X) = 100.68 miles Varianceof Y is, var(Y) = 689.13 $ Now,Correlation between X & Y = 228.93/sqrt(100.68*689.13) = 0.87 Correlation between Gas & Distance is 0.87, which ispossitively correlated. D sol :- If data is converted into miles tokilometers then variance of X becomes 161.09 kilometers andcovariance of Y becomes366.29 kilometers. Thencorrelation between X &Y = 368.43/sqrt(162.03*689.13) = 1.1 It's not exist becuase correlation always lies between -1 to+1. E sol :- For anindividual who lives 18 miles from work then prediction for Gasexpenditure in the regression line is Y = 105.58 + 2.28 (18) =146.62$. Theexpenditure is predicted by 146.62 when an individual lives 18miles from work. F sol :- Eachand every individual spent same dollars at that point i.e.,140.62$. 37 195.83 24 160.86 36 186.14 17 168.93 24 151.16 13 128.67 21 141.09 11 137.29 15 139.85 11 149.69 36 172.54 11 112.69 38 190.62 24 140.06 40 211.2 26 182.24 18 140.62Related Questions
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