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# Week 5 Electronic Text MicroSoft Word Solutions (12.52+12.54+13.26+13.28+14.18) - All work shown + megastat output

CSU - Dominguez hills

GPA 3.0

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Date Created: 11/16/15

12.52 Below are average gestation days and longevity data for 22 animals. (a) Make a scatter plot. (b) Find the correlation coefficient and interpret it. (c) Test the correlation coefficient for significance, clearly stating the degrees of freedom. (Data are from The World Almanac and Book of Facts, 2005, p. 180. Used with permission.) Gestation Gestation (days) and Longevity (Years) for Selected Animals (n = 22) Animal Gestation Longevity Animal Gestation Longevity Animal Gestation Longevity Animal Gestation Longevity Ass 365 12 Horse 330 20 Baboon 187 20 Kangaroo 42 7 Beaver 122 5 Lion 100 15 Buffalo 278 15 Moose 240 12 Camel 406 12 Mouse 21 3 Cat 63 12 Possum 15 1 Dog 61 12 Rabbit 31 5 Deer 201 8 Rhino 450 15 Elephant 645 40 Sheep 154 12 Fox 52 7 Wolf 63 5 Guinea Pig 68 4 Zebra 365 15 a) 45 40 35 30 f(x) = 0.04x + 4.31 25 R² = 0.63 Longevity 20 15 10 5 0 0 100 200 300 400 500 600 700 Gestation r =0.6269 b) r= 0√6269≈0.7918 c) The hypotheses are: . The formula for this test is: D.F.=n−2=22−2=20 r=0.7918 n=22 r =0.6269 This is a two tailed test, so the rejection regions are: Significance level=0.05 ±t 0.0,20±t 0.025,20.086 2 Reject H0 if: z≥2.086∨z≤−2.086 Otherwise we fail to reject. Test statistic: t=r n−2 √[1−r 2 22−2 ¿0.7918√[1−0.6269 ] ¿0.7918 20 √0.3731 ¿0.7918√53.60493165 ¿0.7918∗7.321538885 ¿5.797194489 ≈5.7972 Since the test statistic is greater than the critical value 5.7972>2.086 We reject the null and we can conclude there is a linear relationship between the two variable. 12.54 Consider the following prices and accuracy ratings for 27 stereo speakers. (a) Make a scatter plot of accuracy rating as a function of price. (b) Calculate the correlation coefficient. At α = .05, does the correlation differ from zero? (c) In your own words, describe the scatter plot. (Data are from Consumer Reports 68, no. 11 [November 2003], p. 31. Data are intended for statistical education and not as a guide to speaker performance.) Speakers Price and Accuracy of Selected Stereo Speakers (n = 27) Brand and Model Type Price ($) Accuracy BIC America Venturi DV62si Shelf 200 91 Bose 201 Series V Shelf Shelf 220 100 89 86 Bose 301 Series V Shelf 330 86 Bose 601 Series IV Floor 600 84 Bose Acoustimass 3 Series IV Floor Shelf 3-Pc 700 300 82 94 Bose Acoustimass 5 Series III Shelf 3-Pc 600 94 Boston Acoustics CR75 Shelf 300 90 Boston Acoustics CR85 Shelf 400 86 Boston Acoustics VR-M50 Shelf 700 90 Cambridge Soundworks Model Six Shelf 150 89 Cambridge Soundworks Newton Series M60 Shelf 300 90 Cambridge Soundworks Newton Series M80 Shelf 400 94 Cerwin Vega E-710 Floor 300 90 Jensen Champion Series C-5 Floor 180 86 KLH 911B Shelf 85 82 Klipsch Synergy SB-3 Monitor Shelf 450 79 Pioneer S-DF1-K Shelf 200 88 Pioneer S-DF2-K Shelf 260 88 Polk Audio R20 Shelf 150 83 Polk Audio R30 Floor 300 89 Polk Audio R50 Floor 400 84 PSB Image 2B Shelf 370 88 Sony SS-MB350H Shelf 100 92 Sony SS-MF750H Floor 280 91 Sony SS-X30ED Shelf 500 83 a) f(x) = R² = 0 12 10 8 6 Y 4 2 0 0 2 4 6 8 10 12 X 2 b) R =0.011 R= 0√011=0.10488 c) The hypotheses are: . The formula for this test is: D.F .=n−2=27−2=25 r=0.10488 r =0.011 n=27 This is a two tailed test, so the rejection regions are: Significance level=0.05 ±t0.05=±t 0.025,2086 2 ,20 Reject H0 if: z≥2.086∨z≤−2.086 Otherwise we fail to reject. Test statistic: n−2 t=r [1−r 2 √ t=0.10488 27−2 √1−0.011] t=0.10488 25 √0.989 t=0.10488√(5.2780586) t=0.10488∗5.027728975 t=0.5273082149 t≈0.5273 Since the test statistic is not in the rejection region, we can’t reject the null hypothesis, and we can conclude that is no linear relationship between these two variables. 0.5273≯≯2.086 d) The scatter plot is extremely scattered, meaning there are an equal amount of points which have high v and y ordinates, low x and y ordinates, low x and high y ordinates, and high x and low y ordinates, meaning the best line to fit this would be a line which has a negative slope since it seems that there are more points on the bottom half of the graph than the top half. 13.26 In a model of Ford’s quarterly revenue TotalRevenue = β0 + β1 CarSales + β2 TruckSales + β3 SUVSales + ε, the three predictors are measured in number of units sold (not dollars). (a) Interpret each slope. The β1 represents the amount of car sold. The β2 represents the amount of truck sold. The β3 represents the amount of SUVs sold. (b) Would the intercept be meaningful? The intercept here represents the money they got from other sources other than vehicle sales, like financing of previous vehicle sales, subsidiary payment, and derivate transactions plus more. (c) What factors might be reflected in the error term? Explain. Some factors may be the reselling back to the company of customers who bought their cars. Another factor could be that sale of a vehicle is incorrectly labeled, meaning a SUV was sold but it was recorded as a car. 13.28 A hospital emergency room analyzed n=17,664 hourly observations on its average occupancy rates using six binary predictors representing days of the week and two binary predictors representing the 8-hourwork shift (12 A.M.–8 A.M., 8 A.M.–4 P.M., 4 P.M.–12 A.M.) when the ER census was taken. The fitted regression equation was AvgOccupancy=11.2+1.19 Mon−0.187 Tue−0.785 Wed−0.580 Thu − 0.451 Fri − 0.267 Sat − 4.58 Shift1 − 1.65 Shift2 (SE = 6.18, R2 = .094, R2 adj = .093). (a) Why did the analyst use only six binaries for days when there are 7 days in a week? Using another binary variable would cause the omission of the intercept. By doing, the statistic program would probably give an error to eliminate one binary. (b) Why did the analyst use only two work shift binaries when there are three work shifts? Using another binary variable would cause the omission of the intercept. By doing, the statistic program would probably give an error to eliminate one binary. (c) Which is the busiest day? Saturday (d) Which is the busiest shift? Shift 1 (e) Interpret the intercept. The intercept is the amount of people there are always regardless of the day and/or shift. (f ) Assess the regression’s fit. The regression’s fit is not so good since the R^2 value is quite low, and the R value is about 0.307, which shows almost no correlation at all. 14.18 (a) Plot either receipts and outlays or federal debt and GDP (plot both time series on the same graph). 2400 2200 2000 f(x) = 0.72x + 559.17 R² = 0.7 1800 Y 1600 1400 1200 1000 1000 1200 1400 1600 1800 2000 2200 X 13000 12000 11000 f(x) = 1.64x 76.96 R² = 0.94 10000 9000 Y 8000 7000 6000 5000 4000 2000 3000 4000 5000 6000 7000 8000 X (b) Describe the trend (if any) and discuss possible causes. The first graph shows a possible exponential, but also a polynomial equation with the degrees greater on the top than on the bottom. Same with the second one, it shows a third degree polynomial. (d) Fit an exponential trend to each. 2400 2200 2000 f(x) = 839.09 exp( 0 x ) 1800 R² = 0.76 Y 1600 1400 1200 1000 1000 1200 1400 1600 1800 2000 2200 X 13000 12000 f(x) = 2956.7 exp( 0 x ) 11000 R² = 0.95 10000 9000 Y 8000 7000 6000 5000 4000 2000 3000 4000 5000 6000 7000 8000 X (e) Interpret each fitted trend equation, explaining its implications. Each trend equation is quite good, as the R^2 value is quite high meaning the trend equation is a good fit. These equations show that the higher the receipt or federal debt is, the higher the outlays or the GDP is respectively. (f) To whom is this issue relevant? FedBudget This is a problem for the government of the country this is for, since it shows as the debt increases the GDP increases as well. U.S. Federal Finances, 1990–2004 ($ billions current) Year Receipts Outlays Federal Debt GDP 1990 1,032 1,253 3,206 5,803 1991 1,055 1,324 3,598 5,996 1992 1,091 1,382 4,002 6,338 1993 1,154 1,410 4,351 6,657 1994 1,259 1,462 4,643 7,072 1995 1,352 1,516 4,921 7,398 1996 1,453 1,561 5,182 7,817 1997 1,579 1,601 5,369 8,304 1998 1,722 1,653 5,478 8,747 1999 1,828 1,702 5,606 9,268 2000 2,025 1,789 5,629 9,817 2001 1,991 1,863 5,770 10,128 2002 1,853 2,011 6,198 10,487 2003 1,782 2,160 6,760 11,004 2004 1,880 2,292 7,355 11,728

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