Ch. 4 Regression Analysis: Exploring Associations between Variables Answer Key 4.1 Visualizing Variability with a Scatterplot 1 Compare Scatterplots to Determine Which One Shows a Greater Strength of Association 1) A 2) B 3) C 4) A 5) C 6) There are two possible answers here: (1) The number of crimes committed is the explanatory variable and the number of police on patrol is the response because the amount of crime can explain a need for more or less police officers. (2) The number of police on patrol is the explanatory variable and the amount of crime is the response because the more police that are on patrol could explain a reduction in the amount of crime. 7) Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points. As a treeʹs diameter increases, its volume typically increases as well. 2 Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots 1) C 2) C 3) B 4) A 5) D 6) A 7) A 8) A 9) C 10) D 11) Answers may vary. Example: People who spend more time working out tend to lose more weight.
4.2 Measuring Strength of Association with Correlation 1 Identify and Interpret Correlation in a Scatterplot 1) B 2) C 3) B 4) A 5) B 6) C 7) A 8) A 9) B 10) D 11) C 12) A 13) C 14) C 15) A 16) D 17) B 18) A correlation coefficient will be negative when there is a negative linear trend in a scatterplot. So, as the values of x increase, the values of y tend to decrease. 19) Scatterplot (i) has the highest correlation because it is more linear than scatterplot (ii). The points have less vertical variation in scatterplot (i), so the relationship is stronger. 20) The correlation coefficient, r, will get closer to 1 because the point is an outlier. Since the rest of the points show a strongly positive linear relationship, r would reflect that and get closer to 1. Page 42 Copyright © 2020 Pearson Education, Inc.
