A national consumer magazine reported the following correlations.

The correlation between car weight and car reliability is -0.30.

The correlation between car weight and annual maintenance cost is 0.20.

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.

a. III only
b. I, II, and III
c. I and II
d. I only

Correct option: (b).

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship between the relative movements of the two variables (i.e. dependent and independent). It ranges from -1 to +1.

Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa. A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.

In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.

The closer the correlation value is to 1 the stronger the relationship between the two variables.

Let,

X = car weight

Y = car reliability

Z = annual maintenance cost

It is provided that:

Corr. (X, Y) = -0.30

Corr. (X, Z) = 0.20

The correlation coefficient of car weight and car reliability is negative. This implies that there is a negative relation between the two variables, i.e. as the weight of the car increases the reliability decreases and vice-versa.

And the correlation coefficient of car weight and annual maintenance cost is positive. That is, the two variables move in the same direction, i.e. as the weight of the car increases the annual maintenance cost also increases.

The correlation coefficient value of (X, Y) is closer to 1 than that of (X, Z).

This implies that the relationship between car weight and car reliability is much more stronger that the relationship between car weight and annual maintenance cost.

Thus, all the provided statement are correct.

Hence, the correct option is (b).

the answer to this question is in the pic

f

step-by-step explanation:

f