Witte & Witte, 9ePage 1 of 4 Pages

Chapter 7 Exercises

Chapter 7 Regression

Exercise 1

It has been suggested by researchers (e.g., Nathanson, Paulhus, & Williams, 2005) that personality variables can be used to predict cheating among college students. Let’s say that the diagram shown below depicts the predicted relationship between psychopathic personality and number of cheating incidents.

  1. Predict the number of cheating incidents, given a psychopathic personality score of 20.
  2. Predict the number of cheating incidents, given a psychopathic personality score of 50.
  3. Predict the number of cheating incidents, given a psychopathic personality score of 78.

Answers:

  1. 10
  2. 25
  3. 39

Exercise 2

It has been suggested by researchers (e.g., Crosnoe, 2006) that academic performance can be used to predict alcohol consumption among high school students. Assume that an r of –.54 describes the relationship between academic performance and estimated weekly alcohol consumption. Additional summary information is shown below.

Academic Performance (X) / Weekly Alcohol Consumption in Ounces (Y)
= 70 / = 58
SSx = 8,424 / SSy = 41,091.84
  1. Determine the least squares equation for predicting alcohol consumption from academic performance using the slope and intercept formulas shown below.
  1. Josh’s academic performance is 75. What is his predicted alcohol consumption?
  2. Jim’s academic performance is 92. What is his predicted alcohol consumption?

Answers:

  1. b = -1.19; a = 141.4;
  2. 52.15
  3. 31.92

Exercise 3

Berry and Worthington (2001) carried out research to identify predictors of stress for undergraduates involved in a relationship. They investigated several predictor variables and utilized advanced statistical techniques to analyze the data. In a simplified statement of their results, we can say that one variable that was found to be a significant predictor of relationship stress (measured by salivary cortisol) was trait anger. The data shown below are similar to the data obtained by these authors.

Trait Anger (X) / Relationship Stress (Y) / Predicted Relationship Stress (Y′)
16 / 0.1 / 0.15
20 / 0.3 / 0.17
24 / 0.1 / 0.18
25 / 0.1 / 0.19
28 / 0.3 / 0.20
30 / 0.2 / 0.21
35 / 0.2 / 0.23
39 / 0.3 / 0.25
43 / 0.2 / 0.26
44 / 0.3 / 0.27
  1. Calculate the standard error of estimate for these data assuming that the correlation between anger and stress is r = .47 and SSy = 0.07.
  2. Provide a rough interpretation of the standard error of estimate in the context of this research investigation.

Answers:

a.

b. On average, predicted stress is off by about 0.08.

Exercise 4

Scatterplots for three sets of data are shown below. For which of these data sets would the least squares regression procedure be appropriate? Explain your answers.

Answer:

The regression equation assumes that there is a straight line relationship between the variables. Scatterplots A and B depict straight line relationships. Scatterplot C depicts a curvilinear relationship. Therefore, the regression procedure that you learned in Chapter 7 is appropriate for data sets A and B but not for data set C.

References

Berry, J. W., & Worthington, Jr., E. L. (2001). Forgivingness, relationship quality, stress while imagining relationship events, and physical and mental health. Journal of Counseling Psychology, 48, 447-455.

Crosnoe, R. (2006). The connection between academic failure and adolescent drinking in secondary school. Sociology of Education, 79, 44-60.

Nathanson, C., Paulhus, D. L., & Williams, K. M. (2006). Contemporary Educational Psychology, 31, 97-122.

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