290 Chapter 9 Correlation and Regression
Height Weight Height Weight
68 125 62 108
66 130 63 95
65.5 120 64 125
66 130 68 133
62 131 62 110
62 120 61.75 108
63 118 62.75 112
67 125
9.33 Using your own height and the appropriate regression equation from Exercise 9.31 or 9.32,
predict your own weight. (If you are uncomfortable reporting your own weight, predict
mine—I am 5 8 and weigh 146 pounds.)
a. How much is your actual weight greater than or less than your predicted weight? (You
have just calculated a residual.)
b. What effect will biased reporting on the part of the students who produced the data play
in your prediction of your own weight?
9.34 Use your scatterplot of the data for students of your own gender and observe the size of the
residuals. (Hint: You can see the residuals in the vertical distance of points from the line.)
What is the largest residual for your scatterplot?
9.35 Given a male and a female student who are both 5 6 , how much would they be expected to
differ in weight? (Hint: Calculate a predicted weight for each of them using the regression
equation specific to their gender.)
9.36 The slope (b) used to predict the weights of males from their heights is greater than the
slope for females. Is this significant, and what would it mean if it were?
9.37 In Chapter 2, I presented data on the speed of deciding whether a briefly presented digit was
part of a comparison set and gave data from trials on which the comparison set had con-
tained one, three, or five digits. Eventually, I would like to compare the three conditions
(using only the data from trials on which the stimulus digit had in fact been a part of that
set), but I worry that the trials are not independent. If the subject (myself) was improving as
the task went along, he would do better on later trials, and how he did would in some way
be related to the number of the trial. If so, we would not be able to say that the responses
were independent. Using only the data from the trials labeled Yin the condition in which
there were five digits in the comparison set, obtain the regression of response on trial num-
ber. Was performance improving significantly over trials? Can we assume that there is no
systematic linear trend over time?Discussion Questions
9.38 In a recent e-mail query, someone asked about how they should compare two air pollution
monitors that sit side by side and collect data all day. They had the average reading per mon-
itor for each of 50 days and wanted to compare the two monitors; their first thought was to
run a t test between the means of the readings of the two monitors. This question would ap-
ply equally well to psychologists and other behavioral scientists if we simply substitute two
measures of Extraversion for two measures of air pollution and collect data using both
measures on the same 50 subjects. How would you go about comparing the monitors (or
measures)? What kind of results would lead you to conclude that they are measuring equiv-
alently or differently? This is a much more involved question than it might first appear, so
don’t just say you would run a t test or obtain a correlation coefficient. Sample data that¿ –¿ –