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Chapter 12: Q141SE (page 807)

Explain why stepwise regression is used. What is its value in the model-building process?

Short Answer

Expert verified

Step-wise regression is used to streamline the number of variables used in the model. To build a model with large number of independent variables is very difficult because of the interpretation of multivariable terms and interactions in the model. Therefore, step-wise regression analysis is used to streamline and select the number of variable which explain the data in the best way.

Step by step solution

01

Step wise regression

Step-wise regression is used to streamline the number of variables used in the model.

02

Value in model-building process

To build a model with large number of independent variables is very difficult because of the interpretation of multivariable terms and interactions in the model. Therefore, step-wise regression analysis is used to streamline and select the number of variable which explain the data in the best way.

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Most popular questions from this chapter

Consider the model:

E(y)=β0+β1x1+β2x2+β3x22+β4x3+β5x1x22

where x2 is a quantitative model and

x1=(1receivedtreatment0didnotreceivetreatment)

The resulting least squares prediction equation is

localid="1649802968695" y⏜=2+x1-5x2+3x22-4x3+x1x22

a. Substitute the values for the dummy variables to determine the curves relating to the mean value E(y) in general form.

b. On the same graph, plot the curves obtained in part a for the independent variable between 0 and 3. Use the least squares prediction equation.

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?

Suppose you fit the model y =β0+β1x1+β1x22+β3x2+β4x1x2+εto n = 25 data points with the following results:

β^0=1.26,β^1= -2.43,β^2=0.05,β^3=0.62,β^4=1.81sβ^1=1.21,sβ^2=0.16,sβ^3=0.26, sβ^4=1.49SSE=0.41 and R2=0.83

  1. Is there sufficient evidence to conclude that at least one of the parameters b1, b2, b3, or b4 is nonzero? Test using a = .05.

  2. Test H0: β1 = 0 against Ha: β1 < 0. Use α = .05.

  3. Test H0: β2 = 0 against Ha: β2 > 0. Use α = .05.

  4. Test H0: β3 = 0 against Ha: β3 ≠ 0. Use α = .05.

Suppose you fit the quadratic model E(y)=β0+β1x+β2x2to a set of n = 20 data points and found R2=0.91, SSyy=29.94, and SSE = 2.63.

a. Is there sufficient evidence to indicate that the model contributes information for predicting y? Test using a = .05.

b. What null and alternative hypotheses would you test to determine whether upward curvature exists?

c. What null and alternative hypotheses would you test to determine whether downward curvature exists?

Question: Failure times of silicon wafer microchips. Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer-Level Packaging Conference, November 3–4, 2005). The failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius). The data for one experiment are given in the table. The researchers want to predict failure time (y) based on solder temperature (x).

  1. Construct a scatterplot for the data. What type of relationship, linear or curvilinear, appears to exist between failure time and solder temperature?
  2. Fit the model,E(y)=β0+β1x+β2x2, to the data. Give the least-squares prediction equation.
  3. Conduct a test to determine if there is upward curvature in the relationship between failure time and solder temperature. (use.α=0.05)
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