Chapter 3, Problem R3.2RE

(a)

To determine

To explain the meaning of the term positive association in this context.

Explanation of Solution

It is given that x be depth in meters and y be dive duration in minutes.

Thus, a positive association means that the y -values tends to increase as the x -values increase. So, in this case, this then implies that if the depth increases then the dive duration tends to increase as well.

(b)

To determine

To explain the meaning of the term linear association in this context.

Explanation of Solution

It is given that x be depth in meters and y be dive duration in minutes.

Thus, a linear association means that the y-values tends to change by the constant amount as the x -values increase by one. So, in this case, this then implies that if the depth increases by one meter, then the dive duration tends to change by a constant amount.

(c)

To determine

To explain the meaning of the term strong association in this context.

Explanation of Solution

It is given that x be depth in meters and y be dive duration in minutes.

Thus, a strong association means that the points in the scatterplot deviate very little from the general pattern between the variables and thus there is very clear pattern in the scatterplot of the two variables. So, in this case, this then implies that there is a very clear pattern between the depth and the dive duration in the scatterplot of the two variables.

(d)

To determine

To explain would this change the correlation and the equation of the least square regression line.

Answer to Problem R3.2RE

The correlation remains unchanged but the regression line will be changed.

Explanation of Solution

It is given that x be depth in meters and y be dive duration in minutes.

Thus, the correlation measures the strength of the linear association between the variables. If we interchange the two variables then this does not affect the strength of the linear association between the variables and thus the correlation remains unchanged. The equation of the least square regression line will change because the equation uses the variable y and x thus interchanging them will affect the regression line.