Question

A recent study was conducted to explore the relationship between the weight of a car and miles per gallon (gas mileage). A linear relationship was investigated with the weight of a car serving as the response variable. The coefficient of determination (R2) was reported to be 79.6%.

a) Interpret this value in terms of the variables in this study.
i. There is a fairly strong positive relationship between car weight and miles per gallon.
ii. There is a fairly strong, negative relationship between car weight and miles per gallon.
iii. Gas mieage can be used to explain about 79.6% of the variability in the weight of the car.
iv. The weight of a car can be used to explain about 79.6% of the variability in gas mileage using a linear relationship.
b) For the study, the correlation coefficient R is -0.8921. Interpret this value in terms of the variables in this question.
i. There is a fairly strong positive relationship between car weight and miles per gallon.
ii. There is a fairly strong, negative relationship between car weight and miles per gallon.
iii. Gas mileage can be used to explain about 89.21% of the variability in the weight of the car.
iv. The weight of a car can be used to explain about 89.21% of the variability in gas mileage using a linear relationship.

Answer 1

Answer: a. iv. The weight of a car can be used to explain about 79.6% of the variability in gas mileage using a linear relationship.

b. ii. There is a fairly strong, negative relationship between car weight and miles per gallon.

Explanation:

• A coefficient of determination (denoted by R²) is a measure in a regression model that determines proportion of the variance in the dependent quantity that is predictable from the independent quantity.

• It is square of correlation coefficient (R).

Here, independent quantity = weight of a car

dependent quantity = miles per gallon (gas mileage)

The coefficient of determination (R²) was reported to be 79.6%.

That means, The weight of a car can be used to explain about 79.6% of the variability in gas mileage using a linear relationship.

• A correlation coefficient(R) tells about the strength and direction of relation .
• It lies between -1 and 1.

For the study, the correlation coefficient R is -0.8921.

There is a fairly strong, negative relationship between car weight and miles per gallon.