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Chapter 12: 143SE (page 807)

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model Ey=尾0+尾1x+尾2x2and it will pass exactly through all three points, yielding SSE = 0. The researcher, delighted with the excellent fit of the model, eagerly sets out to use it to make inferences. What problems will he encounter in attempting to make inferences?

Short Answer

Expert verified

The researcher has fit a second-order model to the data and taken one measurement on y at 3 different values for x. The SSE value is coming out to be zero indicating that the data points lie perfectly on the line. However, since the SSE value is zero, the researcher might face issues while testing the significance of beta parameters or the goodness of fit test for the model.

Step by step solution

01

Second-order model

The researcher has fit a second-order model to the data and taken one measurement on y at 3 different values for x. The SSE value is coming out to be zero indicating that the data points lie perfectly on the line.

02

Problems with second-order model

However, since the SSE value is zero, the researcher might face issues while testing the significance of beta parameters or the goodness of fit test for the model.

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Most popular questions from this chapter

It is desired to relate E(y) to a quantitative variable x1and a qualitative variable at three levels.

  1. Write a first-order model.

  2. Write a model that will graph as three different second- order curves鈥攐ne for each level of the qualitative variable.

To model the relationship between y, a dependent variable, and x, an independent variable, a researcher has taken one measurement on y at each of three different x-values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model Ey=尾0+尾1x+尾2x2 and it will pass exactly through all three points, yielding SSE = 0. The researcher, delighted with the excellent fit of the model, eagerly sets out to use it to make inferences. What problems will he encounter in attempting to make inferences?

Question: Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.

Question: Refer to Exercise 12.82.

a. Write a complete second-order model that relates E(y) to the quantitative variable.

b. Add the main effect terms for the qualitative variable (at three levels) to the model of part a.

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 curves of the model have the same shape but different y-intercepts?

e. Under what circumstances will the response curves of the model be parallel lines?

f. Under what circumstances will the response curves of the model be identical?

Question: Revenues of popular movies. The Internet Movie Database (www.imdb.com) monitors the gross revenues for all major motion pictures. The table on the next page gives both the domestic (United States and Canada) and international gross revenues for a sample of 25 popular movies.

  1. Write a first-order model for foreign gross revenues (y) as a function of domestic gross revenues (x).
  2. Write a second-order model for international gross revenues y as a function of domestic gross revenues x.
  3. Construct a scatterplot for these data. Which of the models from parts a and b appears to be the better choice for explaining the variation in foreign gross revenues?
  4. Fit the model of part b to the data and investigate its usefulness. Is there evidence of a curvilinear relationship between international and domestic gross revenues? Try using伪=0.05.
  5. Based on your analysis in part d, which of the models from parts a and b better explains the variation in international gross revenues? Compare your answer with your preliminary conclusion from part c.
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