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Chapter 11: Q1E (page 649)

In each case, graph the line that passes through the given points.

a. (1, 1) and (5, 5) b. (0, 3) and (3, 0)

c. (-1, 1), and (4, 2) d. (-6, -3) and (2, 6)

Short Answer

Expert verified

Fig. 1 Straight line model

Step by step solution

01

Step 1: Introduction.

A straight line is the best approximation for the connection between the dependent and independent variables. The model is no longer simple linear when two or more independent variables are utilized in regression analysis. Multiple regressions are the term for this.

02

Graph the line that passes through (1, 1) and (5, 5),(0, 3) and (3, 0),(-1, 1) and (4, 2)&(-6, -3) and (2, 6).

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Most popular questions from this chapter

Best-paid CEOs. Refer to Glassdoor Economic Research firm’s 2015 ranking of the 40 best-paid CEOs in Table 2.1 (p. 65). Recall that data were collected on a CEO’s age and ratio of salary to a typical worker’s pay at the firm. One objective is to predict the ratio of salary to worker pay based on the CEO’s age.

a. In this study, identify the dependent and independent variables.

b. Explain why a probabilistic model is more appropriate than a deterministic model.

c. Write the equation of the straight-line, probabilistic model.

Do nice guys really finish last in business? Refer to the Nature (March 20, 2008) study of whether “nice guys finish last” in business, Exercise 11.18 (p. 653). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,” where competitors choose cooperation, defection, or costly punishment. At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used for each player. Based on a scatter plot of the data, the simple linear regression relating average payoff (y) to punishment use (x) resulted in SSE = 1.04.

a. Assuming a sample size of n = 28, compute the estimated standard deviation of the error distribution, s.

b. Give a practical interpretation of s.

Congress voting on women’s issues. The American Economic Review (March 2008) published research on how the gender mix of a U.S. legislator’s children can influence the legislator’s votes in Congress. The American Association of University Women (AAUW) uses voting records of each member of Congress to compute an AAUW score, where higher scores indicate more favorable voting for women’s rights. The researcher wants to use the number of daughters a legislator has to predict the legislator’s AAUW score.

a. In this study, identify the dependent and independent variables.

b. Explain why a probabilistic model is more appropriate than a deterministic model.

c. Write the equation of the straight-line, probabilistic model.

Generation Y’s entitlement mentality. The current workforce is dominated by “Generation Y”—people born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job, without the work ethic). The reasons behind this phenomenon were investigated in Proceedings of the Academy of Educational Leadership (Vol. 16, 2011). A sample of 272 undergraduate business students was administered a questionnaire designed to capture the behaviors that lead to an entitlement mentality. The responses were used to measure the following two quantitative variables for each student: entitlement score (y)—where higher scores indicate a greater level of entitlement, and “helicopter parents” score (x)—where higher scores indicate that the student’s parents had a higher level of involvement in his or her everyday experiences and problems.

a. Give the equation of a simple linear regression model relating y to x.

b. The researchers theorize that helicopter parents lead to an entitlement mentality. Based on this theory, would you expect β0 to be positive or negative (or are you unsure)? Would you expect β1 to be positive or negative (or are you unsure)? Explain.

c. The p-value for testing H0: β0 = 0 versus Ha: β1> 0 was reported as .002. Use this result to test the researchers’ entitlement theory at α = .01.

Visually compare the scatter plots shown below. If a least squares line were determined for each data set, which do you think would have the smallest variance s2? Explain.
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