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Chapter 12: Q99E (page 773)

Question: The complete modelE(y)=尾0+尾1x1+尾2x2+尾3x3+尾4x4+蔚was fit to n = 20 data points, with SSE = 152.66. The reduced model,E(y)=尾0+尾1x1+尾2x2+蔚, was also fit, with

SSE = 160.44.

a. How many 尾 parameters are in the complete model? The reduced model?

b. Specify the null and alternative hypotheses you would use to investigate whether the complete model contributes more information for the prediction of y than the reduced model.

c. Conduct the hypothesis test of part b. Use 伪 = .05.

Short Answer

Expert verified

Answer

a. The no. of 尾 parameters in complete model are 5 and the no of 尾 parameters in reduced model are 3.

b. The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as H0: 尾3 = 尾4 = 尾5 = 0 while Ha: At least one of 尾 parameters are nonzero

c. At 95% confidence interval there is enough evidence to not reject H0

Step by step solution

01

No of β parameters

The no. of 尾 parameters in complete model are 4 and the no of 尾 parameters in reduced model are 3.

02

 Step 2: Hypotheses

The null and alternate hypothesis to test whether the complete model contributes more information for the prediction of y than the reduced model can be written as

H0: 尾3 = 尾4 = 0 while Ha: At least one of 尾 parameters are nonzero.

03

Thesis testing

H0: 尾3 = 尾4 = 0 and Ha: At least one of 尾 parameters are nonzero

Teststatistic=((SSER-SSEC)/(k-g))(SSEC/[n-(k-1)])=0.38222

For 伪 = .05, F-test statistic = 3.009. H0 is rejected if F-statistic > F

Here, 0.38222 < 3.009.

Therefore, at 95% confidence interval there is enough evidence to not reject H0.

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Most popular questions from this chapter

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 first-order model relating to

  1. Two quantitative independent variables.
  2. Four quantitative independent variables.
  3. Five quantitative independent variables.

Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3. The ranges of the variables you observed were as follows: 10 鈮� y 鈮� 100, 5 鈮� x1 鈮� 55, 0.5 鈮� x2 鈮� 1, and 1,000 鈮� x3 鈮� 2,000. Will the error of prediction be smaller when you use the least squares equation to predict y when x1 = 30, x2 = 0.6, and x3 = 1,300, or when x1 = 60, x2 = 0.4, and x3 = 900? Why?

Question: Accuracy of software effort estimates. Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates. The dependent variable, defined as the relative error in estimating effort, y = (Actual effort - Estimated effort)/ (Actual effort) was determined for each in a sample of n = 49 software development tasks. Eight independent variables were evaluated as potential predictors of relative error using stepwise regression. Each of these was formulated as a dummy variable, as shown in the table.

Company role of estimator: x1 = 1 if developer, 0 if project leader

Task complexity: x2 = 1 if low, 0 if medium/high

Contract type: x3 = 1 if fixed price, 0 if hourly rate

Customer importance: x4 = 1 if high, 0 if low/medium

Customer priority: x5 = 1 if time of delivery, 0 if cost or quality

Level of knowledge: x6 = 1 if high, 0 if low/medium

Participation: x7 = 1 if estimator participates in work, 0 if not

Previous accuracy: x8 = 1 if more than 20% accurate, 0 if less than 20% accurate

a. In step 1 of the stepwise regression, how many different one-variable models are fit to the data?

b. In step 1, the variable x1 is selected as the best one- variable predictor. How is this determined?

c. In step 2 of the stepwise regression, how many different two-variable models (where x1 is one of the variables) are fit to the data?

d. The only two variables selected for entry into the stepwise regression model were x1 and x8. The stepwise regression yielded the following prediction equation:

Give a practical interpretation of the 尾 estimates multiplied by x1 and x8.

e) Why should a researcher be wary of using the model, part d, as the final model for predicting effort (y)?
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