Car Sales and Sunspots Data Set 25 in Appendix B includes pairs of data for the sunspot number and the number of U.S. car sales for 21 different years. A TI-83 Plus calculator was used to find that the value of the linear correlation coefficient is r 5 20.284.

a. Is there a significant linear correlation between the sunspot number and the number of U.S. car sales? Explain.

b. What proportion of the variation in the number of U.S. car sales can be explained by the variation in the sunspot number?

a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a correlation between x and y.

b. After identifying the 10 pairs of coordinates corresponding to the 10 points, find the value of the correlation coefficient r and determine whether there is a significant linear correlation.

c. Now remove the point with coordinates (10, 10) and repeat parts

(a) and (b).

d. What do you conclude about the possible effect from a single pair of values?
Testing for a Linear Correlation. In Exercises 8–14, construct a scatterplot, find the value of the linear correlation coefficient r and use a significance level of a 5 0.05 to determine whether there is a significant linear correlation between the two variables. Save your work because the same data sets will be used in the next section.