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Chapter 12: 138SE (page 807)

The first-order model E(y)=β0+β1x1was fit to n = 19 data points. A residual plot for the model is provided below. Is the need for a quadratic term in the model evident from the residual plot? Explain.

Short Answer

Expert verified

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x. Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

Step by step solution

01

Residual plot

The residual plot indicates a strong positive relation among dependent and independent variable. And since the residual points are clustered around in a straight line, the graph is indicating a linear relationship among y and x.

02

Need for quadratic term

Since the graph indicates a linear relationship between dependent and independent variable, there is no need for an additional quadratic term in the model.

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Most popular questions from this chapter

Comparing private and public college tuition. According to the Chronicle of Higher Education Almanac, 4-year private colleges charge, on average, five times as much for tuition and fees than 4-year public colleges. In order to estimate the true difference in the mean amounts charged for an academic year, random samples of 40 private colleges and 40 public colleges were contacted and questioned about their tuition structures.

  1. Which of the procedures described in Chapter 8 could be used to estimate the difference in mean charges between private and public colleges?

  2. Propose a regression model involving the qualitative independent variable type of college that could be used to investigate the difference between the means. Be sure to specify the coding scheme for the dummy variable in the model.

  3. Explain how the regression model you developed in part b could be used to estimate the difference between the population means.

Question: Job performance under time pressure. Time pressure is common at firms that must meet hard and fast deadlines. How do employees working in teams perform when they perceive time pressure? And, can this performance improve with a strong team leader? These were the research questions of interest in a study published in the Academy of Management Journal (October, 2015). Data were collected on n = 139 project teams working for a software company in India. Among the many variables recorded were team performance (y, measured on a 7-point scale), perceived time pressure (, measured on a 7-point scale), and whether or not the team had a strong and effective team leader (x2 = 1 if yes, 0 if no). The researchers hypothesized a curvilinear relationship between team performance (y) and perceived time pressure (), with different-shaped curves depending on whether or not the team had an effective leader (x2). A model for E(y) that supports this theory is the complete second-order model:E(y)=β0+β1x1+β2x12+β3x2+β4x1x2+β5x12x2

a. Write the equation for E(y) as a function of x1 when the team leader is not effective (x2= 0).

b. Write the equation for E(y) as a function ofwhen the team leader is effective (x2= 1).

c. The researchers reported the following b-estimates:.

β0^=4.5,β1^=0.13,β3^=0.15,β4^=0.15andβ5^=0.29Use these estimates to sketch the two equations, parts a and b. What is the nature of the curvilinear relationship when the team leaders is not effective? Effective?

Question:Suppose you fit the first-order model y=β0+β1x1+β2x2+β3x3+β4x4+β5x5+εto n=30 data points and obtain SSE = 0.33 and R2=0.92

(A) Do the values of SSE and R2suggest that the model provides a good fit to the data? Explain.

(B) Is the model of any use in predicting Y ? Test the null hypothesis H0:β1=β2=β3=β4=β5=0 against the alternative hypothesis {H}at least one of the parameters β1,β2,...,β5 is non zero.Useα=0.05 .

Consider relating E(y) to two quantitative independent variables x1 and x2.

  1. Write a first-order model for E(y).

  2. Write a complete second-order model for E(y).
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