1. Multiple Choice. The scatterplots below display the relationship between x an

Question

1. Multiple Choice. The scatterplots below display the relationship between x and y for nine different datasets. Note that the sample correlation for each case is displayed as well.

Use the plots and sample correlations above to answer the following questions. Note: In order to get full credit on each of the questions below you need to check all options that apply. No partial credit will be given.

(a) Which datasets have a linear and positive relationship between x and y? List all that apply.

(b) Which datasets have a linear and negative relationship between x and y? List all that apply.

(c) Which datasets have a linear and weak relationship between x and y? List all that apply.

(d) Which datasets have a linear and moderate relationship between x and y? List all that apply.

(e) Which datasets have a linear and strong relationship between x and y? List all that apply.

(f) Which datasets have a nonlinear relationship between x and y? List all that apply.

(g) Which dataset definitely contains outliers? Select the best option.

Dataset A Dataset B Dataset C r = 0.67 r-0.89 r = 0.17 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Dataset D Dataset E Dataset F r=-0.47 r 0.74 r =-0.06 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Dataset G Dataset H Dataset l r=-0.62 r =-0.57 r=0.71 0 20 4060 80 100 0 20 40 60 80 100 0 20 40 60 80 100

Explanation / Answer

In statistics, the correlation coefficient r measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. To interpret its value, see which of the following values your correlation r is closest to:

Exactly –1. A perfect downhill (negative) linear relationship

–0.70. A strong downhill (negative) linear relationship

–0.50. A moderate downhill (negative) relationship

–0.30. A weak downhill (negative) linear relationship

0. No linear relationship

+0.30. A weak uphill (positive) linear relationship

+0.50. A moderate uphill (positive) relationship

+0.70. A strong uphill (positive) linear relationship

Exactly +1. A perfect uphill (positive) linear relationship

a. A, E and H

b. B,G and I

c. C and F

d. D and I

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