O CORRELATION AND SIMPLE LINEAR REGRESSION Alexia Linear relationship and the sample correlation coefficient Espano Below are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale.) Each data set is made up of sample values drawn from a population. x y 1.0 7.1 11 3 1.0 10.0 11 2.0 9.3 2.0 9.0 10 D 3.0 3.9 3.0 8.0 4.0 8.9 4.0 7.0 5.0 5.2 3.0 6.0 6.0 2.4 6.0 5.0 7.0 3.9 7.0 4.0 8.0 10.3 0 12 3 4 3 6 7 8 9Torf 8.0 3.0 0 1 2 3 4 3 6 / 8 gron 9.0 4.9 Figure 1 9.0 2.0 Figure 2 10.0 7.9 10.0 1.0 m n 1.0 7.8 11 1 1.0 2.9 11 1 2.0 8.6 10 2.0 4.0 3.0 6.8 3.0 3.8 4.0 5.3 4.0 5.3 5.0 8.0 5.0 4.5 6.0 5.2 6.0 6.9 3 7.0 4.4 1 7.0 6.0 1 8.0 7.1 0 12343 6 8 91611 8.0 8.0 0 1 2 3 4 5 6 / 8 9 1671 9.0 6.6 Figure 3 9.0 7.0 Figure 4 10.0 3.7 10.0 7.9 Answer the following questions about the relationships between pairs of variables and the values of r, the sample correlation coefficient. The same response may be the correct answer for more than one question. (a) For which data set is the sample correlation coefficient r closest to 0? x ? (Choose one) V (b) Which data set indicates the strongest negative linear relationship between its two variables? (Choose one) V c) For which data set is the sample correlation coefficient r equal to - 1? (Choose one) (d) Which data set has an apparent positive, but not perfect, linear relationship between its two variables? (Choose one) Explanation Check