Question

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6. The following data was extracted from the 1974 Motor Trend US magazine, and com- prises fuel consumption , mpg (response) and 6 aspects of automobile design and per- formance (explanatory variables) for 32 automobiles (1973-74 models). mpg Miles/(US) gallon cyl Number of cylinders disp Displacement (cu.in.) hp Gross horsepower am Transmission (0 = automatic, 1 = manual) 50 150 250 mpg 10 25 200 cyl 00 00000 ood 00 disp 100 400 hp 00000000 am 90 00 por lo 10 20 30 100 300 0.0 0.4 0.8 mpg cyl disp hp am mpg 1.0000000 -0.8521620 -0.8475514 -0.7761684 0.5998324 cyl -0.8521620 1.0000000 0.9020329 0.8324475 -0.5226070 disp -0.8475514 0.9020329 1.0000000 0.7909486 -0.5912270 hp -0.7761684 0.8324475 0.7909486 1.0000000 -0.2432043 am 0.5998324 -0.5226070 -0.5912270 -0.2432043 1.0000000 (a) (4 points) Which explanatory variable is most highly correlated with the response? (b) [6 points] Are there any explanatory variables correlated with each other? If so, which ones? Why is collinearity a concern in multiple linear regression?

Answer 1

Solution

a)

The cyl variable is most highly correlated with response mpg having correlation -0.8521620

b)

Yes,

The disp and cyl, hp and cyl , disp and hp are highly correlated variables, since there are highly correlated with each other so collinearity will concern since the correlation between these variables > 0.7