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Chapter 12: 141SE (page 807)

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

Short Answer

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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

State casket sales restrictions. Some states permit only licensed firms to sell funeral goods (e.g., caskets, urns) to the consumer, while other states have no restrictions. States with casket sales restrictions are being challenged in court to lift these monopolistic restrictions. A paper in the Journal of Law and Economics (February 2008) used multiple regression to investigate the impact of lifting casket sales restrictions on the cost of a funeral. Data collected for a sample of 1,437 funerals were used to fit the model. A simpler version of the model estimated by the researchers is E(y)=β0+β1x1+β2x2+β3x1x2, where y is the price (in dollars) of a direct burial, x1 = {1 if funeral home is in a restricted state, 0 if not}, and x2 = {1 if price includes a basic wooden casket, 0 if no casket}. The estimated equation (with standard errors in parentheses) is:

y^=1432 + 793x1- 252x2+ 261x1x2, R2= 0.78

(70) (134) (109)

  1. Calculate the predicted price of a direct burial with a basic wooden casket at a funeral home in a restricted state.

  2. The data include a direct burial funeral with a basic wooden casket at a funeral home in a restricted state that costs \(2,200. Assuming the standard deviation of the model is \)50, is this data value an outlier?

  3. The data also include a direct burial funeral with a basic wooden casket at a funeral home in a restricted state that costs \(2,500. Again, assume that the standard deviation of the model is \)50. Is this data value an outlier?

Question: Shopping on Black Friday. Refer to the International Journal of Retail and Distribution Management (Vol. 39, 2011) study of shopping on Black Friday (the day after Thanksgiving), Exercise 6.16 (p. 340). Recall that researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits. Two of the variables measured for each shopper were age (x) and number of years shopping on Black Friday (y). Data on these two variables for the 38 shoppers are listed in the accompanying table.

  1. Fit the quadratic model, E(y)=β0+β1x+β2x2, to the data using statistical software. Give the prediction equation.
  2. Conduct a test of the overall adequacy of the model. Use α=0.01.
  3. Conduct a test to determine if the relationship between age (x) and number of years shopping on Black Friday (y) is best represented by a linear or quadratic function. Use α=0.01.

Question: Determine which pairs of the following models are “nested” models. For each pair of nested models, identify the complete and reduced model.

a.E(y)=β0+β1x1+β2x2b.E(y)=β0+β1x1c.E(y)=β0+β1x1+β2x12d.E(y)=β0+β1x1+β2x2+β3x1x2e.E(y)=β0+β1x1+β2x2+β3x1x2+β4x21+β5x22

Question: Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.63 (p. 749). Recall that the failure times of the microchips (in hours) was determined at different solder temperatures (degrees Celsius). The data are repeated in the table below.

  1. Fit the straight-line modelEy=β0+β1xto the data, where y = failure time and x = solder temperature.

  2. Compute the residual for a microchip manufactured at a temperature of 149°C.

  3. Plot the residuals against solder temperature (x). Do you detect a trend?

  4. In Exercise 12.63c, you determined that failure time (y) and solder temperature (x) were curvilinearly related. Does the residual plot, part c, support this conclusion?
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