The following data were collected during a study of consumer buying patterns: Observation Observation 1 11 30 77 8. 23 78 77 9 10 69 44 82 10 19 70 34 84 11 23 87 47 92 12 19 90 42 93 13 32 91 32 79 b. Obtain a linear regression line for the data. (Round your intermediate calculations and final answers to 3 decimal places.) y= c. What percentage of the variation is explained by the regression line? (Do not round intermediate calculations. Round your answer to the nearest whole percent. Omit the "%" sign in your response.) Approximately % of the variation in the dependent variable is explained by the independent variable. d. Use the equation determined in part b to predict the expected value of y for x= 43. (Round your intermediate calculations and final answers to 3 decimal places.) %3D

The following data were collected during a study of consumer buying patterns: Observation Observation 1 11 30 77 8. 23 78 77 9 10 69 44 82 10 19 70 34 84 11 23 87 47 92 12 19 90 42 93 13 32 91 32 79 b. Obtain a linear regression line for the data. (Round your intermediate calculations and final answers to 3 decimal places.) y= c. What percentage of the variation is explained by the regression line? (Do not round intermediate calculations. Round your answer to the nearest whole percent. Omit the "%" sign in your response.) Approximately % of the variation in the dependent variable is explained by the independent variable. d. Use the equation determined in part b to predict the expected value of y for x= 43. (Round your intermediate calculations and final answers to 3 decimal places.) %3D

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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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?
The following data is a regression model where the U.S. Department of Transportation has tried to relate the rate of fatal traffic accidents (per 1000 licenses) to the percentage of motorists under the age of 21. Data has been collected for 42 major cities in the United States. SUMMARY OUTPUT Regression Statistics Multiple R 0.83938748 R Square 0.70457134 Adjusted R Square 0.69718562 Standard Error 0.58935028 Observations 42 ANOVA df SS MS F Regression 1 33.13441764 33.1344 95.3964 Residual 40 13.89335048 0.34733 Total 41 47.02776812 Coefficients Standard Error t Stat P-value Intercept -1.5974138 0.371671454 -4.2979 0.00010 Percent Under 21 0.28705317 0.029389769 9.76711 3.79E-9…
The following table displays the mathematics test scores for a random sample ofcollege students, along with their final SY16C grades.a. Fit the regression line y=a+bx to the data and interpret the results.b. Use the regression equation to determine the SY16C grade for a college student whoscored 60 on their achievement test. What would their SY16C gradebe? Mathematics test(x) SY16C grades(y)1 39 652 43 783 21 524 64 825 57 926 47 897 28 738 75…
A sales manager collected the following data on annual sales for new customer accounts and the number of years of experience for a sample of 10 salespersons. Salesperson Years of Experience Annual Sales ($1000s) 1 1 80 2 3 97 3 4 92 4 4 102 5 6 103 6 8 111 7 10 119 8 10 123 9 11 117 10 13 136 Develop a scatter diagram for these data with years of experience as the independent variable. Develop an estimated regression equation that can be used to predict annual sales given the years of experience. Use the estimated regression equation to predict annual sales for a salesperson with 9 years of experience.
Consider the following computer output from a multiple regression analysis relating the price of a used car to the variables: age of car, mileage, and safety rating. Coefficients Coefficients Standard Error t� Stat P-value Intercept 42465.6942465.69 5320.545320.54 7.9817.981 0.00000.0000 Age (Year) −21096.02−21096.02 2551.522551.52 −8.268−8.268 0.00000.0000 Mileage(in Thousands) −1312.73−1312.73 103.02103.02 −12.743−12.743 0.00000.0000 Safety Rating 1533.821533.82 165.72165.72 9.2559.255 0.00000.0000 Does the sign of the coefficient for the variable safety rating make sense?
The Update to the Task Force Report on Blood Pressure Control in Children [12] reported the observed 90th per-centile of SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of average height are given in Table 11.18. Suppose we seek a more efficient way to display the data and choose linear regression to accomplish this task. age sbp 1 99 2 102 3 105 4 107 5 108 6 110 7 111 8 112 9 114 10 115 11 117 12 120 13 122 14 125 15 127 16 130 17 132 Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Am I supposed to run a residual plot and QQ-plot for this question?
The following data shows the dexterity test scores of five assembly-line employees of Dimples Company Limited and their respective hourly productivity.Employee Score on dexterity test (?) Ali 12Kofi 14Kwesi 17Abudu 16Nana 11Units produced in an hour (?) 55636770 51You are required to(i) Write the regression equation(ii) Interpret the regression equation(iii) Calculate the Pearson’s Product Moment Correlation Coefficient.(iv) Interpret the correlation coefficient (v) Suppose the dexterity test score is 13, what would be the units produced in an hour? (vi) Clearly explain (in detail) the difference between regression analysis and correlation analysis.
The following data on exposure to alpha particles on cell abnormalities. Exposure abnormalities 0.106 2 0.193 5 0.511 13 0.527 15 1.08 25 1.62 28 1.73 36 2.36 45 2.72 56 3.12 59 3.88 63 4.18 60 Construct the scatter plot and compute the regression line Compute the residuals and graph the residual plot Comment on any features you see in these data.
Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume(units) Total Cost($) 400 4,000 450 4,900 550 5,300 600 5,900 700 6,400 750 7,000 This data was used to develop an estimated regression equation, ŷ = 1,121.33 + 7.76x, relating production volume and cost for a particular manufacturing operation. Use ? = 0.05 to test whether the production volume is significantly related to the total cost. (Use the F test.) State the null and alternative hypotheses. -H0: ?1 ≠ 0Ha: ?1 = 0 -H0: ?1 ≥ 0Ha: ?1 < 0 -H0: ?0 ≠ 0Ha: ?0 = 0 -H0: ?1 = 0Ha: ?1 ≠ 0 -H0: ?0 = 0Ha: ?0 ≠ 0 Set up the ANOVA table. (Round your p-value to three decimal places and all other values to two decimal places.) Sourceof Variation Sumof Squares Degreesof Freedom MeanSquare F p-value Regression ? ? ? ? ? Error ? ? ? Total ? ? Find the value of the test statistic. (Round your answer to two decimal places.) Test…
A specialist in hospital administration stated that no. of employees in a hospital can be estimated by counting the no. of beds in the hospital .A health care researcher decided to develop a regression model in an attempt to predict the number of employees of a hospital by the no. of beds . 12 hospitals were surveyed and obtained following data. No of Beds. Employees 23 69 29 95 29 102 35 118 42 126 46 125 50 138 54 178 64 156 66 184 76 176 78 225 After obtaining the regression model and interpret it accordingly based on your understanding. Explain the…
The grades of a class of 9 students on a midterm report (x) and on the final examination (y) are as follows: Give the following: a. linear regression line and equation b. computation of the coefficient of determination ?^2 c. Computation of the coefficient of correlation ? d. Estimate the final examination grade of a student who received a grade of 85 on the midterm report.