Chapter PII, Problem 14RE

(a)

To determine

To find out which two variables in the table exhibit the strongest association.

Answer to Problem 14RE

Weight and displacement are two variables.

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 two variables in the table exhibit the strongest association are weight and displacement as their correlation is strong.

(b)

To determine

To explain is that strong association necessarily cause and effect and offer at least two explanations why that association might be so strong.

Answer to Problem 14RE

That is not a strong association necessarily cause and effect.

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, that is not a strong association necessarily cause and effect because some larger vehicles will be heavier so may need more cylinders to move the vehicles. Certain vehicles will have many cylinders and will take up more space and be heavier.

(c)

To determine

To explain how would changing from cubic inches to litres affect the calculated correlations involving displacement.

Answer to Problem 14RE

This may not change.

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 changing from cubic inches to litres this may not affect the calculated correlations involving displacement as correlation is not affected by units.

(d)

To determine

To explain what would you predict about the fuel efficiency of a car whose engine displacement is one standard deviation about the mean.

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, we will predict about the fuel efficiency of a car whose engine displacement is one standard deviation about the mean as the fuel efficiency will be one standard deviation below the mean.