EBK BUSINESS STATISTICS
7th Edition
ISBN: 8220102743984
Author: STEPHAN
Publisher: PEARSON
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(4) Does how wide a possum's belly is (in cm) tell you how long a possum's tail is (in cm)? That's what re-
searchers in Australia wanted to know. They built a simple linear regression model treating X as the possum's
belly girth and Y as the possum's tail length. Below and at the top of the next page are all the results you will
need to answer the ensuing questions, including:
● The straight line of best fit: ŷ
= 30.2 + .21x
• The correlation between the observed y and predicted ŷ: ry,ŷ
.294
• At the top of the next page are three residual plots: (a) the plot of belly girth vs. the residuals, (b) the plot
of the residuals in order of collection, (c) the histogram of the residuals
=
These are real data (source) consisting of measurements on each of 104 mountain brushtail possums, trapped
at seven sites from Southern Victoria to central Queensland, Australia.
1. Develop a simple linear regression equation for starting salaries using an independent
variable that has the closest relationship with the salaries. Explain how you chose this
variable.
The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below.
The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive?
Is the regression coefficient statistically significant? How can you tell?
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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardTable 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?arrow_forward
- Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardSuppose you wanted to test whether or not the payoff to an additional year of education was the same for men and women in the STEM majors. How would you set up your regression analysis in this casearrow_forwardThe following equation is the result of performing a multiple regression analysis: Job performance = 10 + (5*job knowledge) + (0.7* conscientiousness), where job knowledge is measured on a scale of 0-5 and conscientiousness is measured on a scale of 0 to 100. Which of the following conclusions is correct? !! O If a person scored 5 on job knowledge and 100 on conscientiousness he or she would have the maximum predictive score possible If a person scored 0 on both job knowledge and conscientiousness, his or her predictive score is 0 ONeither job knowledge nor conscientiousness predicts performance O Conscientiousness is less important than job knowledge. Question 3! For a measuring tool to be usefulitmus bearrow_forward
- In the method of regression, data sets are summarized in a useful form. The “independent” pieces of data are called inputs or regressors, whereas a quantity that is a function of the inputs, will be called a response. In an experiment, the effect of increasing storage temperature is related to the number of spoiled loaves of bread after 7 days. In this case, which variable will be the regressor?arrow_forwardThe follow table gives the approximate economic value associated with various levels of oil recovery in Texas. Find the regression line, and use it to estimate the economic value associated with a recovery level of 70%.arrow_forwardThe operations manager of a musical instrument distributor feels that the demand for Bass Drums may be related to the number of television appearances by the popular rick group Green Shades during the previous month. The manager has collected the data shown in the following table. Demand for Bass Drums 3 6 7 5 10 8 Green Shades TV appearances 3 4 7 6 8 5 Develop the linear regression equation to forecast. Forecast demand for Bass Drums when Green Shades’ TV appearances are 10. Compute MSE and standard deviation for Problem 8.arrow_forward
- The following table gives the amount spent on cellular service. Date Cellular service revenue(in billions) 2011 1.01 2012 1.05 2013 1.09 2014 1.11 Plot the data points. (Let tbe the number of years since 2011 and C the amount of cellular service revenue, in billions of dollars.) CORRECT (b) Find the equation of the regression line. (Let t be the number of years since 2011 and C the amount of cellular service revenue, in billions of dollars. Round the regression line parameters to three decimal places.) C(t) = C(t) = 0.034t+1.014 CORRECT Add its graph to the plotted data. CORRECT (c) In 2015, $1.14 trillion was spent on cellular service. If you had been a financial strategist in 2014 with only the data in the table above available, what would have been your prediction for the amount spent on cellular service in 2015? (Round your answer to two decimal places.) billion dollars CORRECT…arrow_forwardSuppose a researcher collects data on houses that have been sold in a particular neighbourhood over the past year, and obtains the regressions results in the table shown below. A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?arrow_forwardThe U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. What proportion of variation in the number of complaints can be explained by hourly wages? From the results shown above, write the regression equation If wages were increased by $1.00, what is the expected effect on the number of complaints received per employee?arrow_forward
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