Chapter 11: Q31E (page 661)
Visually compare the scatter plots shown below. If a least squares line were determined for each data set, which do you think would have the smallest variance ? Explain.
Graph (c)
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Refer to Exercise 2.18 and calculate the number of the 600 items falling into each of the classes. Then graph a frequency histogram for these data.
Generation Yโs entitlement mentality. The current workforce is dominated by โGeneration Yโโpeople born between 1982 and 1999. These workers have a reputation as having an entitlement mentality (e.g., they believe they have a right to a high-paying job, without the work ethic). The reasons behind this phenomenon were investigated in Proceedings of the Academy of Educational Leadership (Vol. 16, 2011). A sample of 272 undergraduate business students was administered a questionnaire designed to capture the behaviors that lead to an entitlement mentality. The responses were used to measure the following two quantitative variables for each student: entitlement score (y)โwhere higher scores indicate a greater level of entitlement, and โhelicopter parentsโ score (x)โwhere higher scores indicate that the studentโs parents had a higher level of involvement in his or her everyday experiences and problems.
a. Give the equation of a simple linear regression model relating y to x.
b. The researchers theorize that helicopter parents lead to an entitlement mentality. Based on this theory, would you expect ฮฒ0 to be positive or negative (or are you unsure)? Would you expect ฮฒ1 to be positive or negative (or are you unsure)? Explain.
c. The p-value for testing H0: ฮฒ0 = 0 versus Ha: ฮฒ1> 0 was reported as .002. Use this result to test the researchersโ entitlement theory at ฮฑ = .01.
Refer to Exercise 11.14 (p. 653). Calculate SSE and s for the least-squares line. Use the value of s to determine where most of the errors of prediction lie.
If a straight-line probabilistic relationship relates the mean E(y) to an independent variable x, does it imply that every value of the variable y will always fall exactly on the line of means? Why or why not?
Voltage sags and swells. The power quality of a transformer is measured by the quality of the voltage. Two causes of poor power quality are "sags" and "swells." A sag is an unusual dip and a swell is an unusual increase in the voltage level of a transformer. The power quality of transformers built in Turkey was investigated in Electrical Engineering (Vol. 95, 2013). For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184. Assume the standard deviation of the sag distribution is 30 sags per week and the standard deviation of the swell distribution is 25 swells per week.
a. For a sag distribution with any shape, what proportion of transformers will have between 263 and 443 sags per week? Which rule did you apply and why?
b. For a sag distribution that is mound-shaped and symmetric, what proportion of transformers will have between 263 and 443 sags per week? Which rule did you apply and why?
c. For a swell distribution with any shape, what proportion of transformers will have between 109 and 259 swells per week? Which rule did you apply and why?
d. For a swell distribution that is mound-shaped and symmetric, what proportion of transformers will have between 109 and 259 swells per week? Which rule did you apply and why?
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