The Statistical Imagination, 2nd Edition 1 Answers

Chapter 14 Answers to Chapter Questions: The Statistical Imagination, 2nd Edition 1 Answers to End-of-Chapter Questions for Chapter 14 Solutions Manual to Accompany The Statistical Imagination: Elementary Statistics for the Social Sciences by Ferris J. Ritchey 2nd edition, McGraw-Hill, 2008/2009 by Brian P. Hinote, Jason Wasserman and Ferris J. Ritchey Questions for Chapter 14 are on page 538 of the text. 1. With the help of a hand-sketched scatterplot and the regression equation explain the central idea behind regression analysis. The central idea behind regression analysis is to use the formula of a straight line to improve best estimates of an interval/ratio dependent variable (Y ) for all values of an interval/ratio independent variable (X ). Without knowledge that X is correlated with Y, the best estimate of Y for any value of X is the mean of Y. With knowledge of a relationship between variables, however, we can predict to the regression line rather than the mean line. This is illustrated with a scatterplot Figure CQ14-1 below. If we had no idea that horsepower was related to engine size, to estimate horsepower all we could do is predict the value of the mean, which is represented by the flat line just above a horsepower of 100. But if we know that horsepower is related to engine size, we can improve our estimates by predicting to the regression line, the line that slopes upward. For example, we can estimate that engines with over 400 cubic inches tend to have horsepowers around 200. In fact, with the regression formula we can make rather precise estimates of Y for any given value of X. Chapter 14 Answers to Chapter Questions: The Statistical Imagination, 2nd Edition 2 Figure CQ14-1. Scatterplot of Automobile Engine Horsepower Regressed on Size of Engine 2. With the help of hand-sketched scatterplots, illustrate why linear correlation and regression analysis applies only when there is a cigar-shaped, linear pattern of coordinates.