Question

stat hw unit 3: linear regression and correlation score: 22/50 answered: 5/9 question 6 a national consumer magazine reported the following correlations. the correlation between car weight and car reliability is - 0.9. the correlation between car weight and annual maintenance cost is 0.6. according to this information, which of the following statements are true? i. heavier cars tend to be less reliable. ii. heavier cars tend to cost more to maintain. iii. car weight is related more strongly to reliability than to maintenance cost. i only ii only iii only i and ii i, ii, and iii

Explanation:

Step1: Analyze correlation between weight and reliability

The correlation coefficient between car weight and car reliability is - 0.9. A negative correlation coefficient means that as one variable (car weight) increases, the other variable (car reliability) decreases. So heavier cars tend to be less reliable.

Step2: Analyze correlation between weight and maintenance cost

The correlation coefficient between car weight and annual maintenance cost is 0.6. A positive correlation coefficient means that as car weight increases, annual maintenance cost also increases. So heavier cars tend to cost more to maintain.

Step3: Compare the magnitudes of correlation coefficients

The magnitude of - 0.9 (correlation between weight and reliability) is 0.9, and the magnitude of 0.6 (correlation between weight and maintenance cost) is 0.6. Since 0.9>0.6, car weight is related more strongly to reliability than to maintenance cost.

Answer:

E. I, II, and III