2.99 See Answer

Question: A regression model to predict Y, the

A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage.
A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. 


(a). Calculate the t statistic for each coefficient to test for βj = 0. 
(b). Look up the critical value of Student’s t in Appendix D for a two-tailed test at α = .01. Which coefficients differ significantly from zero? 
(c). Use Excel to find a p-value for each coefficient.

Use Appendix D:

(a). Calculate the t statistic for each coefficient to test for βj = 0. (b). Look up the critical value of Student’s t in Appendix D for a two-tailed test at α = .01. Which coefficients differ significantly from zero? (c). Use Excel to find a p-value for each coefficient. Use Appendix D:
A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. 


(a). Calculate the t statistic for each coefficient to test for βj = 0. 
(b). Look up the critical value of Student’s t in Appendix D for a two-tailed test at α = .01. Which coefficients differ significantly from zero? 
(c). Use Excel to find a p-value for each coefficient.

Use Appendix D:





Transcribed Image Text:

Predictor Coefficient SE Intercept AgeMed Bankrupt FedSpend HSGrad% 4,198.5808 799.3395 -27.3540 12.5687 17.4893 12.4033 -0.0124 0.0176 -29.0314 7.1268 Confidence Level Confidence Level .80 .90 .95 .98 .99 .80 .90 .95 .98 .99 Significance Level for Two-Tailed Test Significance Level for Two-Tailed Test 20 .10 .05 .02 .01 20 .10 .05 .02 .01 Significance Level for One-Tailed Test Significance Level for One-Tailed Test d.f. .10 .05 .025 .01 .005 d.f. .10 .05 .025 .01 .005 31.821 6.965 4.541 3.747 3.078 6.314 12.706 63.657 36 1.306 1.688 2.028 2.434 2.719 2 1.886 2.920 2.353 2.132 4.303 3.182 2.776 9.925 37 1.305 1.687 1.686 1.685 2.026 2.431 2.715 1.638 4 1.533 5.841 4.604 38 39 1.304 1.304 2.712 2.708 2.024 2.023 2.021 2.429 2.426 2.423 5 1.476 2.015 2.571 3.365 4.032 40 1.303 1.684 2.704 1.943 1.895 1.860 2.020 2.018 2.017 6 1.440 2.447 3.143 3.707 41 1.303 1.683 2.421 2.701 2.365 2.306 2.998 42 1.302 1.682 1.681 1.680 7 1.415 3.499 3.355 2.418 2.416 2.414 2.412 2.698 1.397 9 1.383 2.896 43 1.302 2.695 3.250 3.169 1.833 2.262 2.821 44 1.301 2.015 2.692 10 1.372 1.812 2.228 2.764 45 1.301 1.679 2.014 2.690 1.363 1.356 2.201 3.106 1.679 1.678 1.677 11 1.796 1.782 2.718 2.681 46 1.300 2.013 2.012 2.410 2.687 12 2.1 3.055 47 1.300 48 1.299 2.40 2.685 13 1.350 2.650 1.771 1.761 2.160 3.012 2.011 2.407 2.405 2.403 2.682 2.680 14 1.677 1.345 15 1.341 2.145 2.624 2.977 49 1.299 2.010 1.753 2.131 2.602 2.947 50 1.299 1.676 2.009 2.678 16 2.921 1.337 1.333 1.746 2.120 2.583 55 1.297 1.673 2.004 2.396 2.668 2.390 2.385 17 1.740 2.110 2.567 2.898 60 1.296 1.671 2.000 2.660 18 1.330 1.734 2.101 2.552 2.878 65 1.295 1.669 1.997 1.994 2.654 19 1.328 1.729 2.093 2.539 2.861 70 1.294 1.667 2.381 2.648 20 1.325 1.725 2.086 2.528 2.845 75 1.293 1.665 1.992 2.377 2.643 1.323 1.321 1.664 1.663 21 1.721 2.080 2.518 2.831 80 1.292 1.990 2.374 2.639 2.819 2.807 22 1.717 2.074 2.508 85 1.292 1.988 2.371 2.635 23 1.319 1.714 2.069 2.500 90 1.291 1.662 1.987 2.368 2.632 2.366 2.364 24 1.318 1.711 2.064 2.492 2.797 95 1.291 1.661 1.985 2.629 25 1.316 1.708 2.060 2.485 2.787 100 1.290 1.660 1.984 2.626 1.659 1.658 1.657 26 1.315 1.706 2.056 2.479 2.779 110 1.289 120 1.289 130 1.982 2.361 2.621 27 28 1.314 1.313 1.703 1.701 2.052 2.048 2.473 2.467 2.771 2.763 1.980 1.978 2.358 2.355 2.617 2.614 1.288 1.656 1.655 2.353 2.351 29 1.311 1.699 2.045 2.462 2.756 140 1.288 1.977 2.611 30 1.310 1.697 2.042 2.457 2.750 150 1.287 1.976 2.609 31 1.309 1.696 2.040 2.453 2.744 1.282 1.645 1.960 2.326 2.576 32 1.309 1.694 2.037 2.449 2.738 33 1.308 1.692 2.035 2.445 2.733 34 1.307 1.691 2.032 2.030 2.441 2.728 35 1.306 1.690 2.438 2.724



> Use MINITAB’s Stat > Basic Statistics > Normality Test or other software to obtain a probability plot for the Ashoka Curry House carry-out order data (see Exercise 15.16). Interpret the probability plot and Anderson-Darling statis

> Refer to the freezer problem 17.51 with μ = 23 and σ = 2. Temperature measurements are recorded four times a day (at midnight, 0600, 1200, and 1800). Twenty samples of four observations are shown below. Problem 17.51: The tem

> Refer back to the regression equation in exercise 12.14: Credits = 15.4 - .07 Work. (a) Calculate the residual for the x, y pair (14, 18). Did the regression equation underestimate or overestimate the credits? (b) Calculate the residual for the x, y pair

> Refer to the paint thickness problem 17.49. Assume μ = 1.00 and σ = 0.07. Use the following 35 individual observations on paint thickness to answer the questions posed. Problem 17.49: In painting an automobile at the factory,

> Concerning confidence intervals, which statement is most nearly correct? Why not the others? a. We should use z instead of t when n is large. b. We use the Student’s t distribution when σ is unknown. c. Using the Student’s t distribution instead of z na

> In painting an automobile at the factory, the thickness of the color coat has a process mean of 1.00 mil and a process standard deviation of 0.07 mil. Twenty samples of five cars were tested, resulting in the mean paint thicknesses shown below. (a). C

> Refer to the bolt strength problem 17.47. Assume μ = 6,050 and σ = 100. Use the following 24 individual bolt strength observations to answer the questions posed. Problem 17.47: The yield strength of a metal bolt has a mean of

> The yield strength of a metal bolt has a mean of 6,050 pounds with a standard deviation of 100 pounds. Twenty samples of three bolts were tested, resulting in the means shown below. (a). Construct upper and lower control limits for the chart, using th

> Refer back to the regression equation in exercise 12.12: NetIncome = 2,277 + .0307 Revenue. Recall that the variables are both in millions of dollars. (a) Calculate the residual for the x, y pair ($41,078, $8,301). Did the regression equation underestima

> A regression model to predict the price of a condominium for a weekend getaway in a resort community included the following predictor variables: number of nights needed, number of bedrooms, whether the condominium complex had a swimming pool or not, and

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> Define (a) productivity, (b) quality control, and (c) process control.

> Why are the control limits for an R chart asymmetric, while those of an  chart are symmetric?

> Which statement is false? Explain. a. If P(A) = .05, then the odds against event A’s occurrence are 19 to 1. b. If A and B are mutually exclusive events, then P (A ∪ B) = 0. c. The number of permutations of 5 things taken 2 at a time is 20.

> Bob said, “They must not be using quality control in automobile manufacturing. Just look at the J.D. Power data showing that new cars all seem to have defects.” (a) Discuss Bob’s assertion, focusing on the concept of variation. (b) Can you think of proce

> Define three quality metrics that might be used to describe quality and performance in the following consumer products: (a) your personal vehicle (e.g., car, SUV, truck, bicycle, motorcycle); (b) the printer on your computer; (c) the toilet in your bathr

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> (a) Plot the data on leisure and hospitality employment. (b) Describe the trend (if any) and discuss possible causes. (c) Fit the linear and exponential trends. Would these trend models give credible forecasts? Explain. (d) Make a forecast for 2008, usin

> For each of the following fitted trends, make a prediction for period t = 17: a. yt = 2286 e.076t b. yt = 1149 + 12.78t c. yt = 501 + 18.2t - 7.1t2

> In a test of the regression model Y = β0 + β1X with 27 observations, what is the critical value of t to test the hypothesis that β1 = 0 using α = .05 in a two-tailed test? a. 1.960 b. 2.060 c. 1.708

> Based on the information in this ANOVA table, the coefficient of determination R2 is a. 0.499 b. 0.501 c. 0.382 ANOVA Table Source Sum of Squares df Mean Square F p-Value 158.3268 Regression Residual 1 158.3268 24.88 0.00004 159.0806 25 6.3632 To

> Which statement is incorrect? Explain. a. Correlation uses a t-test with n - 2 degrees of freedom. b. Correlation analysis assumes that X is independent and Y is dependent. c. Correlation analysis is a test for the degree of linearity between X and Y.

> Given a sample correlation coefficient r = .373 with n = 30, can you reject the hypothesis ρ = 0 for the population at α = .01? Explain, stating the critical value you are using in the test.

> Given the following ANOVA: (a). How many ATM locations were there? (b). What was the sample size? (c). At α = .05, is there a significant effect due to Day of Week? (d). At α = .05, is there a significant interaction?

> If P (A) = .30, P (B) = .70, and P (A ∩ B) = .25, are A and B independent events? Explain.

> Given the following ANOVA table, find the F statistic and the critical value of F.05. Source Sum of Squares df Mean Square F Treatment 744.00 4. Error 751.50 15 Total 1,495.50 19

> Which statement is incorrect? Explain. a. We need a Tukey test because ANOVA doesn’t tell which group means differ. b. Hartley’s test is needed to determine whether the means of the groups differ. c. ANOVA assumes equal variances in the k groups being c

> In this regression with n = 40, which predictor differs significantly from zero at α = .01? a. X2 b. X3 c. X5 Coefficients Std. Error Intercept 3.210610 0.918974 X1 -0.034719 0.023283 X2 0.026794 0.039741 X3 -0.048533 0.000272 0.009

> Which predictors differ significantly from zero at α = .05? a. X3 only b. X4 only c. both X3 and X4 Coefficients Std. Error p-Value Intercept X1 23.3015 4.1948 0.0000 0.2100 -0.227977 0.178227 X2 0.218970 0.300784 0.4719 X3 -0.34365

> Which predictor coefficients differ significantly from zero at α = .05? a. X3 and X5 b. X5 only c. all but X1 and X3 Coefficients Std. Error Lower 95% Upper 95% Intercept 22.47427 6.43282 9.40122 35.54733 X1 -0.243035 0.162983 -0.57

> For a multiple regression, which statement is false? Explain. a. If R2 = .752 and R2 adj = .578, the model probably has at least one weak predictor. b. R2 adj can exceed R2 if the model contains some very strong predictors. c. Deleting a predictor could

> (a) Plot the data on skier/snowboard visits. (b) Would a fitted trend be helpful? Explain. (c) Make a forecast for 2007–2008, using a trend model of your choice (or a judgment forecast). U.S. Skier/Snowboarder Visits, 1984-2007 (mi

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> Given n1 = 8, s1 = 14, n2 = 12, s2 = 7. (a). Find the test statistic for a test for equal population variances. (b). At α = .05 in a two-tailed test, state the critical value and degrees of freedom.

> For the following contingency table, find (a) P (H &acirc;&#136;&copy; T); (b) P (S | G); (c) P(S) R Row Total 10 50 30 90 H 20 50 40 110 Col Total 30 100 70 200

> Which statement is correct concerning the normal approximation? Why not the others? a. The normal Poisson approximation is acceptable when λ > 10. b. The normal binomial approximation is better when n is small and π is large. c. Normal approximations are

> In a random sample of 200 Colorado residents, 150 had skied at least once last winter. A similar sample of 200 Utah residents revealed that 140 had skied at least once last winter. At α = .025, is the percentage significantly greater in Colorado? Explain

> Which of the following Excel formulas would be a correct way to calculate P(X < 450) given that X is N(500, 60)? a. =NORM.DIST(450, 500, 60, 1) b. =NORM.S.DIST(450, 60) c. =1–NORM.DIST(450, 500, 60, 0)

> A consulting firm used a random sample of 12 CIOs (chief information officers) of large businesses to examine the relationship (if any) between salary (in thousands) and years of service in the firm. (a). Make a scatter plot and describe it. (b). Calc

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> Find the mean, standard deviation, and coefficient of variation for X = 5, 10, 20, 10, 15.

> Which statement is incorrect? Explain. a. If p = .50 and n = 100, the estimated standard error of the sample proportion is .05. b. In a sample size calculation for estimating π, it is conservative to assume π = .50. c. If n = 250 and p = .07 it is not s

> Which statement is false? Explain. a. To find probabilities in a continuous distribution, we add up the probabilities at each point. b. A uniform continuous model U(5,21) has mean 13 and standard deviation 4.619. c. A uniform PDF is constant for all valu

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> A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. (a). State the hypotheses to test whether the mean transaction time exceeds 60 seconds. (b). Find the test statistic. (c). At α = .02

> Which statement is not correct? Explain. a. The sample data x1, x2, . . . , xn will be approximately normal if the sample size n is large. b. For a skewed population, the distribution of / is approximately normal if n is large. c. The expected value of /

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> A sample of 74 Noodles & Company restaurants was used to perform a regression analysis with Y = % Annual Revenue Growth and X = % Revenue Due to Loyalty Card Use. Calculate the leverage statistic for the following three restaurants and state whether or n

> A sample of season performance measures for 29 NBA teams was collected for a season. A regression analysis was performed on two of the variables with Y = total number of free throws made and X = total number of free throws attempted. Calculate the levera

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> In the previous problem, calculate (a) the 95th percentile of vehicle speeds (i.e., 95 percent below); (b) the lowest 10 percent of speeds; (c) the highest 25 percent of speeds (3rd quartile).

> (a) Make an Excel scatter plot. What does it suggest about the population correlation between X and Y? (b) Make an Excel worksheet to calculate SSxx, SSyy, and SSxy. Use these sums to calculate the sample correlation coefficient. Check your work by using

> Review the two residual plots below. Do either of these show evidence that the regression error assumptions of normality and constant variation have been violated? Explain. X -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 Normal Score Residual Residuals

> Review the two residual plots below. Do either of these show evidence that the regression error assumptions of normality and constant variation have been violated? Explain. -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 Normal Score Residual

> Study the table of residuals. Identify as outliers any standardized residuals that exceed 3 and as unusual any that exceed 2. Can you suggest any reasons for these unusual residuals? Midterm and Final Exam Scores for Business Statistics Students Fall S

> Refer to the Revenue and Profit data set below. Data are in billions of dollars. (a) Use MegaStat or MINITAB to find confidence and prediction intervals for Y using the following set of x values: 1.8, 15, and 30. (b) Report the 95 percent confidence inte

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> (a) Use Excel’s Data Analysis > Regression (or MegaStat or MINITAB) to obtain regression estimates. (b) Interpret the 95 percent confidence interval for the slope. Does it contain zero? (c) Interpret the t test for the slope and its p-value. (d) Interpre

> (a) Use Excel’s Data Analysis > Regression (or MegaStat or MINITAB) to obtain regression estimates. (b) Interpret the 95 percent confidence interval for the slope. Does it contain zero? (c) Interpret the t test for the slope and its p-value. (d) Interpre

> (a) Use Excel&acirc;&#128;&#153;s Data Analysis &gt; Regression (or MegaStat or MINITAB) to obtain regression estimates. (b) Interpret the 95 percent confidence interval for the slope. Does it contain zero? (c) Interpret the t test for the slope and its

> Below is a regression using X = average price, Y = units sold, n = 20 stores. (a) Write the fitted regression equation. (b) Write the formula for each t statistic and verify the t statistics shown below. (c) State the degrees of freedom for the t tests a

> Below is a regression using X = home price (000), Y = annual taxes (000), n = 20 homes. (a) Write the fitted regression equation. (b) Write the formula for each t statistic and verify the t statistics shown below. (c) State the degrees of freedom for the

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> (a) Based on the R2 and ANOVA table for your model, how would you assess the fit? (b) Interpret the p-value for the F statistic. (c) Would you say that your model&acirc;&#128;&#153;s fit is good enough to be of practical value? Midterm and Final Exam S

> (a) Perform a regression using MegaStat or Excel. (b) State the null and alternative hypotheses for a two-tailed test for a zero slope. (c) Report the p-value and the 95 percent confidence interval for the slope shown in the regression results. (d) Is th

> (a) Perform a regression using MegaStat or Excel. (b) State the null and alternative hypotheses for a two-tailed test for a zero slope. (c) Report the p-value and the 95 percent confidence interval for the slope shown in the regression results. (d) Is th

> Using the “Metals” data, construct a correlation matrix of the six independent variables. The response variable is Priceylb. (a). Identify any pairs of independent variables that have a significant pairwise correlation. (b). Using MegaStat or MINITAB,

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2.99

See Answer