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Chapter 11: Q1E (page 649)

In each case, graph the line that passes through the given points.

a. (1, 1) and (5, 5) b. (0, 3) and (3, 0)

c. (-1, 1), and (4, 2) d. (-6, -3) and (2, 6)

Short Answer

Expert verified

Fig. 1 Straight line model

Step by step solution

01

Step 1: Introduction.

A straight line is the best approximation for the connection between the dependent and independent variables. The model is no longer simple linear when two or more independent variables are utilized in regression analysis. Multiple regressions are the term for this.

02

Graph the line that passes through (1, 1) and (5, 5),(0, 3) and (3, 0),(-1, 1) and (4, 2)&(-6, -3) and (2, 6).

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Most popular questions from this chapter

Minitab was used to generate the following histogram:

a. Is this a frequency histogram or a relative frequency histogram? Explain.

b. How many measurement classes were used in the construction of this histogram?

c. How many measurements are in the data set described by this histogram?

Motivation and right-oriented bias. Evolutionary theory suggests that motivated decision makers tend to exhibit a right-oriented bias. (For example, if presented with two equally valued detergent brands on a supermarket shelf, consumers are more likely to choose the brand on the right.) In Psychological Science (November 2011), researchers tested this theory using data on all penalty shots attempted in World Cup soccer matches (totaling 204 penalty shots). The researchers believed that goalkeepers, motivated to make a penalty-shot save but with little time to make a decision, would tend to dive to the right. The results of the study (percentages of dives to the left, middle, or right) are provided in the table. Note that the percentages in each row corresponding to a particular match situation add to 100%. Use graphs to illustrate the distribution of dives for the three-match situations. What inferences can you draw from the graphs?

Source: Based on M. Roskes et al., "The Right Side? Under Time Pressure, Approach Motivation Leads to Right-Oriented Bias," Psychological Science, Vol. 22, No. 11, November 2011 (adapted from Figure 2)11

Construct a scatterplot for the data in the following table.

X

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y

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a. Plot the following two lines on your scatterplot: y = 3 - x and y = 1 + x

b. Which of these lines would you choose to characterize the relationship between x and y? Explain.

c. Show that the sum of the prediction errors for both of these lines equals 0.

d. Which of these lines has the smaller SSE?

e. Determine the data's least-squares line and compare it to the two lines described in part a.

Generation Y’s entitlement mentality. The current workforce is dominated by “Generation Y”—people 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)—where higher scores indicate a greater level of entitlement, and “helicopter parents” score (x)—where higher scores indicate that the student’s 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 β0 to be positive or negative (or are you unsure)? Would you expect β1 to be positive or negative (or are you unsure)? Explain.

c. The p-value for testing H0: β0 = 0 versus Ha: β1> 0 was reported as .002. Use this result to test the researchers’ entitlement theory at α = .01.

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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