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Chapter 12: 126E (page 803)

Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004) study of the accuracy of new software effort estimates, Exercise 12.114 (p. 781). Recall that stepwise regression was used to develop a model for the relative error in estimating effort (y) as a function of company role of estimator (x1 = 1 if developer, 0 if project leader) and previous accuracy (x8 = 1 if more than 20% accurate, 0 if less than 20% accurate). The stepwise regression yielded the prediction equationy^=0.12-0.28x1+0.27x8. The researcher is concerned that the sign of the estimated β multiplied by x1 is the opposite from what is expected. (The researcher expects a project leader to have a smaller relative error of estimation than a developer.) Give at least one reason why this phenomenon occurred.

Short Answer

Expert verified

The estimated sign for β for x1 is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x1. A possible reason for the same could be the existence of multicollinearity in the model.

Step by step solution

01

Reason for opposite sign

The estimated sign for β for x1 is positive (the developer has a larger relative error of estimation than a project leader) but the prediction equation estimated using step-wise regression is negative sign of x1. A possible reason for the same could be the existence of multicollinearity in the model.

02

Rationale behind opposite sign

Since there is high degree of correlation amongst relative error in estimating effort (y) and company role of estimator (x1) the β estimates will not be true parameter indicators and will be biased.

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Most popular questions from this chapter

Service workers and customer relations. A study in Industrial Marketing Management (February 2016) investigated the impact of service workers’ (e.g., waiters and waitresses) personal resources on the quality of the firm’s relationship with customers. The study focused on four types of personal resources: flexibility in dealing with customers(x1), service worker reputation(x2), empathy for the customer(x3), and service worker’s task alignment(x4). A multiple regression model was employed used to relate these four independent variables to relationship quality (y). Data were collected for n = 220 customers who had recent dealings with a service worker. (All variables were measured on a quantitative scale, based on responses to a questionnaire.)

a) Write a first-order model for E(y) as a function of the four independent variables. Refer to part

Which β coefficient measures the effect of flexibility(x1)on relationship quality (y), independently of the other

b) independent variables in the model?

c) Repeat part b for reputation(x2), empathy(x3), and task alignment(x4).

d) The researchers theorize that task alignment(x4)“moderates” the effect of each of the other x’s on relationship quality (y) — that is, the impact of eachx, x1,x2, orx3on y depends on(x4). Write an interaction model for E(y) that matches the researchers’ theory.

e) Refer to part d. What null hypothesis would you test to determine if the effect of flexibility(x1)on relationship quality (y) depends on task alignment(x4)?

f) Repeat part e for the effect of reputation(x2)and the effect of empathy(x3).

g) None of the t-tests for interaction were found to be “statistically significant”. Given these results, the researchers concluded that their theory was not supported. Do you agree?

Consider a multiple regression model for a response y, with one quantitative independent variable x1 and one qualitative variable at three levels.

a. Write a first-order model that relates the mean response E(y) to the quantitative independent variable.

b. Add the main effect terms for the qualitative independent variable to the model of part a. Specify the coding scheme you use.

c. Add terms to the model of part b to allow for interaction between the quantitative and qualitative independent variables.

d. Under what circumstances will the response lines of the model in part c be parallel?

e. Under what circumstances will the model in part c have only one response line?

Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (January 2005) study of a high-pressure inlet fogging method for a gas turbine engine, Exercise 12.19 (p. 726). Recall that you fit a first-order model for heat rate (y) as a function of speed (x1) , inlet temperature (x2) , exhaust temperature (x3) , cycle pressure ratio (x4) , and airflow rate (x5) . A Minitab printout with both a 95% confidence interval for E(y) and prediction interval for y for selected values of the x’s is shown below.

a. Interpret the 95% prediction interval for y in the words of the problem.

b. Interpret the 95% confidence interval forE(y)in the words of the problem.

c. Will the confidence interval for E(y) always be narrower than the prediction interval for y? Explain.

Buy-side vs. sell-side analysts’ earnings forecasts. Refer to the Financial Analysts Journal (July/August 2008) comparison of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 112). The Harvard Business School professors used regression to model the relative optimism (y) of the analysts’ 3-month horizon forecasts. One of the independent variables used to model forecast optimism was the dummy variable x = {1 if the analyst worked for a buy-side firm, 0 if the analyst worked for a sell-side firm}.

a) Write the equation of the model for E(y) as a function of type of firm.

b) Interpret the value ofβ0in the model, part a.

c) The professors write that the value ofβ1in the model, part a, “represents the mean difference in relative forecast optimism between buy-side and sell-side analysts.” Do you agree?

d) The professors also argue that “if buy-side analysts make less optimistic forecasts than their sell-side counterparts, the [estimated value ofβ1] will be negative.” Do you agree?

Question: Adverse effects of hot-water runoff. The Environmental Protection Agency (EPA) wants to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area. The goal is to acquire a prediction equation for the number of marine animals located at certain designated areas, or stations, in the gulf. Based on past experience, the EPA considered the following environmental factors as predictors for the number of animals at a particular station:

X1 = Temperature of water (TEMP)

X2 = Salinity of water (SAL)

X3 = Dissolved oxygen content of water (DO)

X4 = Turbidity index, a measure of the turbidity of the water (TI)

x5 = Depth of the water at the station (ST_DEPTH)

x6 = Total weight of sea grasses in sampled area (TGRSWT)

As a preliminary step in the construction of this model, the EPA used a stepwise regression procedure to identify the most important of these six variables. A total of 716 samples were taken at different stations in the gulf, producing the SPSS printout shown below. (The response measured was y, the logarithm of the number of marine animals found in the sampled area.)

a. According to the SPSS printout, which of the six independent variables should be used in the model? (Use α = .10.)

b. Are we able to assume that the EPA has identified all the important independent variables for the prediction of y? Why?

c. Using the variables identified in part a, write the first-order model with interaction that may be used to predict y.

d. How would the EPA determine whether the model specified in part c is better than the first-order model?

e.Note the small value of R2. What action might the EPA take to improve the model?
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