Question

The table shows a short excerpt from the "car weight and mileage" data file on the text CD. That file lists several 2004 model cars with automatic transmission and their x = weight (in pounds) and y = mileage (miles per gallon of gas). The scatterplot is roughly linear and r = -0.86. The regression equation is û = 49.586 -0.0058x. Automobile Brand Honda Accord Sedan LX Toyota Corolla Dodge Dakota Club Cab Jeep Grand Cherokee Laredo Hummer H2 Weight Mileage 3103 33 2638 40 3857 22 4018 21 6399 16 (a) Find the predicted mileage and residual for a Hummer H2. (2 decimal places) Residual = (2 decimal places) (b) Use this information in a sentence. The Hummer gets miles/gallon ---Select-- than one would predict. (c) % (Enter a number between 0 and 100; 2 decimal places) of the variability in --Select--- can be explained by ---Select---

Answer 1

a).the predicted mileage for a Hummer H2 be:-

$\hat{y}=49.586-(0.0058*6399)\approx \mathbf{12.47}$

the residual be:-

$=y_{observed}-\hat{y}$

== 16-12.47

$=\mathbf{3.53}$

b). The hummer gets 3.53 miles/gallon more than one would predict.

c). coefficient of determination be:-

$R^2=(r)^2=(-0.86)^2=0.7396=73.96\%$

73.96 % of the variability in mileage (y) can be explained by weight (x).

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