answer b c and d. 1. Use the data given to solve the following problems.Savings needed for Health-Care Expenses During RetirementAge at DeathSavings Needed80$219,00085$307,00090$409,00095$524,000100$656,000Source: Employee Benefit Research Instituteb.) Use tne graphing utility's regression option to compare the following models: y=ab",y= a + blnx, y= ax+b, and y = axb. Submit a sketch or image of each.c.) Discuss how each of the regression curves in part b fit the data by looking at thecorrelation constant r.d.) Use the model (equation) with the best correlation constant, r from part c and predictby which year the population will reach 315 million.

1. Use the data given to solve the following problems. Savings needed for Health-Care Expenses During Retirement Age at Death Savings Needed 80 $219,000 85 $307,000 90 $409,000 95 $524,000 100 $656,000 Source: Employee Benefit Research Institute

1. Use the data given to solve the following problems. Savings needed for Health-Care Expenses During Retirement Age at Death Savings Needed 80 $219,000 85 $307,000 90 $409,000 95 $524,000 100 $656,000 Source: Employee Benefit Research Institute

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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?
Consider the following linear regression model that relates income per capita in thousand dollars of a country i (GDP P Ci), with its percentage of the population in the agricultural sector (P Ai): Model : GDP P Ci = β0 + β1P Ai + ui (a) Explain in words how to interpret parameters β0 and β1. What sign do you think these parameters might have? Explain. (b) Draw the (population) regression line associated with this model assuming that parameters β0 and β1 have the sign you have indicated in answering question (2a). Explain the meaning of this regression line.
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergent (R). The marketing director collects 36 weekly observations on S, A and R to estimate the following multiple regression equation: S = a + bA + cR .where, S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10% level or better.DEPENDENT VARIABLE: S R-SQUARE F-RATIO P-VALUE ON FOBSERVATIONS: 36 0.2247 4.781 0.0150VARIABLE PARAMETER STANDARD T-RATIO P-VALUE ESTIMATE ERRORINTERCEPT 175086.0 63821.0 2.74 0.0098A 0.8550 0.3250…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate.The slope tells us the decrease in the number of education doctorates for each additional social science doctorate. The slope tells us the increase in the number…
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + cR where S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. a. What sign does the marketing director expect a, b, and c to have? b. Interpret the coefficeints a, b, and c. The regression output from the computer is as follows: c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate…
The director of marketing at Vanguard Corporation believes that sales of the company’s Bright Side laundry detergent (S) are related to Vanguard’s own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + cR. where S, A, and R are measured in dollars per week. Vanguard’s marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. What sign does the marketing director expect a, b, and c to have? Interpret the coefficients a, b, and c. The regression output from the computer is as follows: 3- Does Vanguard’s advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate p-value. 4- Does advertising by its three largest rivals affect sales of…
The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditure (A), as well as the combined advertising expenditures of its three biggest rival detergents (R). The marketing director collects 36 weekly observations on S, A, and R to estimate the following multiple regression equation: S = a + bA + cR where S, A, and R are measured in dollars per week. Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. a. What sign does the marketing director expect a, b, and c to have? b. Interpret the coefficeints a, b, and c. The regression output from the computer is as follows: c. Does Vanguard's advertising expenditure have a statistically significant effect on the sales of Bright Side detergent? Explain, using the appropriate…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number of social science doctorates for each additional education doctorate. The slope tells us the increase in the number of social science doctorates for each additional education doctorate.…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =