Question

Scatterplots Match these values of r with the five scatterplots shown below: 0.268, 0.992, -1, 0.746, and 1.

Short answer

The r values for the five scatterplots are:

1. $r=-1$
2. $r=0.746$
3. $r=0.268$
4. $r=0.992$
5. $r=1$

Step-by-step solution

Given information

Five scatterplots (a),(b),(c),(d),(e) are given along with five measures of correlation coefficients.

Procedure to estimate values of r from scatterplots

The value of correlation is between -1 and 1. The signs + or – indicate that there is direct and indirect linear association between the pair of variables.

A scatterplot is a graph that shows the paired observations where one variable is scaled

Relationship between scatterplot and value of r

The magnitude shows the strength of linear association between the pair of variables.

If the value is equal to 0, it indicates that there is no association between the variables. The scatter plot shows a random pattern in this case.

As the value approaches 1 or -1, the pattern of observations in scatterplot aligns in a straight line (either upward or downward).Depending on the alignment of the these observations about a straight line the measure of correlation changes.

Evaluating each scatterplot

(a) The scatter plot has all observations aligned about a straight line that slopes downward. Thus, the value of r is estimated to be -1.

(b) The scatter plot has all observations are aligned close to a straight line that slopes upwards. Thus, the value of r is estimated between 0 to 1. Thus, the value of r is estimated to be 0.746.

(c) The scatter plot has observations assigned randomly on the graph. Thus, the value of r is estimated to be very low but positive. In this case, it can take be estimated as 0.268.

(d) The scatter plot has observations aligned close to a straight line pattern in an upward direction. Thus, the value of ris expected to be very close to +1. In this case, it can take be estimated as 0.992.

(e) The scatter plot has observations perfectly aligned about the straight line in upward direction. Thus, the value of r is estimated to be 1.