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Chapter 12: Q134SE (page 807)

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?

Short Answer

Expert verified

Therefore, when predicting y values, the error of prediction will be smaller when x1 = 30, x2 = 0.6, and x3 = 1300 since the values of independent variables are well within the range described in the question.

Step by step solution

01

Range of independent variables

The range of x1, x2, and x3is given as 5 鈮� x1鈮� 55, 0.5 鈮� x2鈮� 1, and 1,000 鈮� x3鈮� 2,000. When x1= 30, x2= 0.6, and x3= 1300, all the variables x1,x2and x3are well within the range of values. While when x1= 60, x2= 0.4, and x3= 900, x1and x2are out of the range and x3is within the range.

02

Conclusion

Therefore, when predicting y values, the error of prediction will be smaller when x1 = 30, x2 = 0.6, and x3 = 1300.

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Most popular questions from this chapter

Question: Consumer behavior while waiting in line. The Journal of Consumer Research (November 2003) published a study of consumer behavior while waiting in a queue. A sample of n = 148 college students was asked to imagine that they were waiting in line at a post office to mail a package and that the estimated waiting time is 10 minutes or less. After a 10-minute wait, students were asked about their level of negative feelings (annoyed, anxious) on a scale of 1 (strongly disagree) to 9 (strongly agree). Before answering, however, the students were informed about how many people were ahead of them and behind them in the line. The researchers used regression to relate negative feelings score (y) to number ahead in line (x1) and number behind in line (x2).

a.The researchers fit an interaction model to the data. Write the hypothesized equation of this model.

b. In the words of the problem, explain what it means to say that 鈥渪1 and x2 interact to affect y.鈥�

c. A t-test for the interaction 尾 in the model resulted in a p-value greater than 0.25. Interpret this result.

d. From their analysis, the researchers concluded that 鈥渢he greater the number of people ahead, the higher the negative feeling score鈥� and 鈥渢he greater the number of people behind, the lower the negative feeling score.鈥� Use this information to determine the signs of 尾1 and 尾2 in the model.

Suppose you fit the second-order model y=尾0+尾1x+尾2x2+蔚to n = 25 data points. Your estimate of尾2is尾^2= 0.47, and the estimated standard error of the estimate is 0.15.

  1. TestH0:尾2=0againstHa:尾2鈮�0. Use伪=0.05.
  2. Suppose you want to determine only whether the quadratic curve opens upward; that is, as x increases, the slope of the curve increases. Give the test statistic and the rejection region for the test for伪=0.05. Do the data support the theory that the slope of the curve increases as x increases? Explain.

Question:Suppose you fit the first-order model y=尾0+尾1x1+尾2x2+尾3x3+尾4x4+尾5x5+蔚to n=30 data points and obtain SSE = 0.33 and R2=0.92

(A) Do the values of SSE and R2suggest that the model provides a good fit to the data? Explain.

(B) Is the model of any use in predicting Y ? Test the null hypothesis H0:尾1=尾2=尾3=尾4=尾5=0 against the alternative hypothesis {H}at least one of the parameters 尾1,尾2,...,尾5 is non zero.Use伪=0.05 .

Comparing private and public college tuition. According to the Chronicle of Higher Education Almanac, 4-year private colleges charge, on average, five times as much for tuition and fees than 4-year public colleges. In order to estimate the true difference in the mean amounts charged for an academic year, random samples of 40 private colleges and 40 public colleges were contacted and questioned about their tuition structures.

  1. Which of the procedures described in Chapter 8 could be used to estimate the difference in mean charges between private and public colleges?

  2. Propose a regression model involving the qualitative independent variable type of college that could be used to investigate the difference between the means. Be sure to specify the coding scheme for the dummy variable in the model.

  3. Explain how the regression model you developed in part b could be used to estimate the difference between the population means.
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