Chapter PII, Problem 13RE

(a)

To determine

To find out which factor seems most strongly associated with fuel efficiency.

Answer to Problem 13RE

Weight seems most strongly associated with fuel efficiency.

Explanation of Solution

It is given in the question that researchers wants to find out that what factor most explains differences in Fuel efficiency among cars. And a correlation matrix exploring the relationship for the car’s weight, horsepower, engine size and number of cylinders is also given. Thus, by looking at the correlation matrix we can see that the weight of the car seems most strongly associated with fuel efficiency as the correlation of weight is strong among all.

(b)

To determine

To explain what does the negative correlation indicate.

Explanation of Solution

It is given in the question that researchers wants to find out that what factor most explains differences in Fuel efficiency among cars. And a correlation matrix exploring the relationship for the car’s weight, horsepower, engine size and number of cylinders is also given. Thus, a negative correlation indicates that as one increases other one decreases this imply that as weight increases MPG decreases.

(c)

To determine

To explain the meaning of $R^2$ for that relationship.

Explanation of Solution

It is given in the question that researchers wants to find out that what factor most explains differences in Fuel efficiency among cars. And a correlation matrix exploring the relationship for the car’s weight, horsepower, engine size and number of cylinders is also given. Thus, the meaning of $R^2$ for that relationship is that $81.54\%$ of the variability of MPG is accounted for by weight.