Chapter 4.5, Problem 26E

To determine

To match: Each graph with its correlation coefficient and explain reasoning.

Answer to Problem 26E

$\text{Graph a}\text{. matches to correlation coefficient B,}$ $r=0.98$ .

$\text{Graph b}\text{. matches to correlation coefficient C,}$ $r=-0.97$ .

$\text{Graph c}\text{. matches to correlation coefficient A,}$ $r=0$ .

$\text{Graph d}\text{. matches to correlation coefficient D,}$ $r=0.69$ .

Explanation of Solution

Given information: Four graphs and correlation coefficients are given.

$\text{Graph a}\text{. matches to correlation coefficient B,}$ $r=0.98$ . Because there is a positive slope, points are making an uphill from left and right, out of the four graphs the points lie most close to the line in this graph, that’s why correlation coefficient closest to $1$ is chosen.

$\text{Graph b}\text{. matches to correlation coefficient C,}$ $r=-0.97$ . Because there is a negative slope, it is the only graph in which points are making a downhill, that’s why negative correlation coefficient is chosen.

$\text{Graph c}\text{. matches to correlation coefficient A,}$ $r=0$ . As the points are neither making an uphill nor downhill, their best line of fit would nearly coincide with horizontal axis. There is no correlation, therefore correlation coefficient of $0$ magnitude is chosen.

$\text{Graph d}\text{. matches to correlation coefficient D,}$ $r=0.69$ . Because there is a positive slope, but all points don’t lie quite close to the line. Overall, points are making an uphill from left and right, that’s why correlation coefficient that is inclined towards $1$ is chosen.