An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383-394) described a study investigating the relationship between noise exposure and hypertension. The following data are representative of those reported in the article. y 10 1 2 5 1 4 6 3 5 46 8 4 5797 6 x 60 63 65 70 70 70 80 90 80 80 85 89 90 90 90 90 94 100 100 100 (a) Test for significance of regression using a = 0.05. What is the P-value for this test? Round to 7 decimal places. (b) Estimate the standard errors of the slope and intercept. Standard error of the slope = i . (Round to four decimal places.) Standard error of the intercept = i . (Round to three decimal places.) (c) Test Ho: Bo = 0 versus H1: Bo # 0 using a = 0.05. Find the P-value for this test. i (Round to six decimal places.)
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- Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver’s credit score, and safety rating of the car. Coefficients Coefficients Standard Error tt Stat P-value Intercept 841841 85.9385.93 9.7879.787 0.00000.0000 Car Accidents(In last 3 years) 151.38151.38 15.9815.98 9.4739.473 0.00000.0000 Credit Score −92.51−92.51 10.2310.23 −9.043−9.043 0.00000.0000 Safety Rating −164.66−164.66 15.9815.98 −10.304−10.304 0.00000.0000 Does the sign of the coefficient for the variable credit score make sense?A random sample of 9 statistics students produced the following data, Midterm Exam Score, x Final Exam Score, y 81 49 62 23 76 84 26 58 96 33 38 36 10 15 15 83 81 28 where x measures the midterm exam score and y measures the final exam score. What is the estimate of the y = a x + b regression intercept coefficient?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.
- The authors of a paper were interested in how the distance a deer mouse will travel for food is related to the distance from the food to the nearest pile of debris. Distances were measured in meters. The data and computer output are given below. Distance from Debris Distance Traveled 6.94 0.00 5.23 6.13 5.21 11.29 7.10 14.35 8.16 12.03 5.50 22.72 9.19 20.11 9.05 26.16 9.36 30.65 Simple Linear Regression Results: Dependent Variable: Traveled Independent Variable: Debris Sample size: 9 R (correlation coefficient) = 0.5657 R-sq = 0.32002088 Estimate of error standard deviation 8.670711 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -7.6854587 13.332196 ≠ 0 7 -0.5764586 0.5824 Slope 3.2340908 1.7818117 ≠ 0 7 1.8150575 0.1124 a)What is the least squares regression line for the output given above? b) what is the predicted traveled distance given the distance from debris is 6.5 meters?For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x. X 6 12 14 6 9 13 15 9 Y 300 408 560 252 288 650 630 522 (a) Determine the least-squares regression line and interpret its slope(b) For an employee who has been with the firm 10 years, what is the predicted number of shares owned? (c) Is there a statistical significance between years of service and ownership of company stocks? (use α=0.05α=0.05)A random sample of 9 statistics students produced the following data, Midterm Exam Score, x Final Exam Score, y 18 87 84 75 48 10 22 60 46 60 92 46 69 33 93 45 28 60 where x measures the midterm exam score and y measures the final exam score. What is the estimate of the y = a x + b regression slope coefficient?
- 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…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…A company trains its employees with instructional videos and claims that the amount of time, in hours, spent training is linearly related to an increase in productivity. The company selected a random sample of five employees to test its claim. The data were used to create the computer output for a least-squares linear regression, shown in the table. Variable DF Estimate SE Intercept 1 3.6 1.1489 Hours 1 0.8 0.3464 Which of the following is the correct test statistic and number of degrees of freedom? t=2.31 with 4 degrees of freedom A t=2.31 with 3 degrees of freedom B t=2.31 with 5 degrees of freedom C t=3.13 with 1 degree of freedom D t=3.13 with 3 degrees of freedom E
- A random sample of twelve students were chosen, and their midterm test score (y), as- signment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 74 76 90 85 87 94 98 81 91 76 74 65 50 55 65 55 70 65 70 55 70 50 55 5 7 5 2 6 3 2 5 4 3 1 4 (i) What is the fitted multiple linear regression equation of the form yˆ = b0 + b1x1 + b2x2? (ii) From part (i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes.A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.It is believed that standardized test scores, such as SAT, is a good predictor of first-year college students' GPA. x 1200 1120 1000 1420 1280 750 1100 y 3.2 2.5 2.7 3.5 2.9 2.2 2.3 1. Find the the correlation coefficient. Round your final answer to four decimal places.r=0.82602. Write the regression equation below. Round all numbers to four decimal places.ˆy=y^=0.0018x+0.6888 3. Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places. 2.98 4. What percentage of variation in GPAs can be explained by students' SAT scores? Round your final answer to two decimal places.