Chapter 12.1, Problem 1E

To determine

To Predict:

The type and strength of the linear relationship between each pair of variables in “Height and shoe size”: weak negative, strong negative, weak positive, strong positive or no linear relationship at all.

Answer to Problem 1E

Solution:

Strong positive

Explanation of Solution

The points in the scatter plot roughly follow a straight-line pattern. The two variables appear to have a linear relationship.

Positive linear relationship:

The direction of the pattern tells how the variables respond to each other. A positive slope indicates that as the values of one variable increase, so do the values of the other variable.

Negative linear relationship:

A negative slope indicates that as the values of one variable increase, the values of the other variable decrease.

The strength of the linear relationship is determined by how closely the points in the scatter plot resemble a straight line.

In the stronger relationship, the diagram looks like a straight line.

In the weaker relationship, the points are more scattered and the diagram doesn’t look like a straight line.

Calculation:

Given that Height and shoe size

As the height increases, the shoe size is usually higher.

The scatter plot of height versus shoe size shows a predictable pattern.

That is, it shows that shoe size seems to increase as height increases.

The two variables appear to have a linear relationship, meaning that the points in the scatter plot roughly follow a straight-line pattern.

Thus, the scatter plot would have a positive slope.

The type of the linear relationship between the variables in “Height and shoe size” is positive.

The strength of the linear relationship between the variables in “Height and shoe size” is strong.

Final statement:

Therefore, the type and strength of the linear relationship between the variables in “Height and shoe size” can be predicted as strong positive.