Below are four bivariate data sets and the scatter plot for each. (Note that eac

Question

Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population.

4.5

3.0m

m

1. For which data set is the sample correlation coefficient r equal to -1?

Choose one (the x, y data set, the u, v data set, the w, t data set, the m, n data setnone of the data sets)

2. Which data set has an apparent positive, but not perfect, linear relationship between its two variables?

Choose one (the x, y data set, the u, v data set, the w, t data set, the m, n data set, none of the data sets)

3. Which data set indicates the strongest positive linear relationship between its two variables?

Choose one (the x, y data set, the u, v data set, the w, t data set, the m, n data set)

4. For which data set is the sample correlation coefficient r closest to 0?

Choose one (the x, y data set, the u, v data set, the w, t data set, the m, n data set)

x y 1.0 1.0 2.0 2.0 3.0 3.0 4.0 4.0 5.0 5.0 6.0 6.0 7.0 7.0 8.0 8.0 9.0 9.0 10.0 10.0

Explanation / Answer

The correlation values are, using technology,

r(xy) = 1

r(uv) = 0.627756409

r(wt) = -0.938604656

r(mn) = 0.017360211

Note that the closer the value of |r| to 1, the stronger the linear relationship. Note also that the sign of r indicates positive/negative relationship.

Hence,

********************************

1. NONE (mn is close, but not -1)

2. UV

3. XY

4. MN

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