D4 Demand for oil changes at Garcia's Garage has been as follows:MonthJanuaryFebruaryMarchAprilMayJune58JulyAugust54a. Use simple linear regression analysis to develop a forecasting model for monthly demand. In this application, the dependent variable, Y. is monthly demand andthe independent variable, X. is the month. For January, let X-1; for February, let X=2; and so on.The forecasting model is given by the equation Y=+x. (Enter your responses rounded to two decimal places)Number of Oil Changes34503889288360455356

Given data is Month Number of Oil changes January 34 February 50 March 60 April 45 May…

Answered: Demand for oil changes at Garcia's…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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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?
Suppose a study wants to predict the market price of a certain species of turtle (Y) based on the following independent variables indicated in the table. Based from the table, what is the equation of the multiple linear regression? (Round off up to two decimal places. Market Price = 0.07 - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 + 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 - 0.40 + weight + 1.51 + length + 1.41 + width + 0.80 + age
Demand for oil changes at Garcia’s Garage has been asfollows:Month Number of Oil ChangesJanuary 41February 46March 57April 52May 59June 51July 60August 62a. Use simple linear regression analysis to develop a fore-casting model for monthly demand. In this application,the dependent variable, Y, is monthly demand and theindependent variable, X, is the month. For January, letX = 1; for February, let X = 2; and so on.b. Use the model to forecast demand for September,October, and November. Here, X = 9, 10, and 11,respectively.
Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income. Hours per week Yearly Income ('000's) 18 43.8p 13 44.5 18 44.8 25.5 46.0 11.5 41.2 18 43.3 16 43.6 27 46.2 27.5 46.8 30.5 48.2 24.5 49.3 32.5 53.8 25 53.9 23.5 54.2 30.5 50.5 27.5 51.2 28 51.5 26 52.6 25.5 52.8 26.5 52.9 33 49.5 15 49.8 27.5 50.3 36 54.3 27 55.1 34.5 55.3 39 61.7 37 62.3 31.5 63.4 37 63.7 24.5 55.5 28 55.6 19 55.7 38.5 58.2 37.5 58.3 18.5 58.4 32 59.2 35 59.3 36 59.4 39 60.5 24.5 56.7 26 57.8 38 63.8 44.5 64.2 34.5 55.8 34.5 56.2 40 64.3 41.5 64.5 34.5 64.7 42.3 66.1 34.5 72.3 28 73.2 38…
Finally, the researcher considers using regression analysis to establish a linear relationship between the two variables – hours worked per week and yearly income. Hours per week Yearly Income ('000's) 18 43.8p 13 44.5 18 44.8 25.5 46.0 11.5 41.2 18 43.3 16 43.6 27 46.2 27.5 46.8 30.5 48.2 24.5 49.3 32.5 53.8 25 53.9 23.5 54.2 30.5 50.5 27.5 51.2 28 51.5 26 52.6 25.5 52.8 26.5 52.9 33 49.5 15 49.8 27.5 50.3 36 54.3 27 55.1 34.5 55.3 39 61.7 37 62.3 31.5 63.4 37 63.7 24.5 55.5 28 55.6 19 55.7 38.5 58.2 37.5 58.3 18.5 58.4 32 59.2 35 59.3 36 59.4 39 60.5 24.5 56.7 26 57.8 38 63.8 44.5 64.2 34.5 55.8 34.5 56.2 40 64.3 41.5 64.5 34.5 64.7 42.3 66.1 34.5 72.3 28 73.2 38…
Midgett Co. has accumulated data to use in preparing its annual profit plan for the upcoming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff suggested that linear regression be employed to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis are as follows: Month MaintenanceCost Machine Hours Jan. $ 5,000 600 Feb. 3,644 440 Mar. 4,400 610 Apr. 3,337 480 May 5,222 660 June 3,390 410 July 3,618 470 Aug. 5,384 630 Sept. 5,114 590 Oct. 4,883 590 Nov. 3,925 430 Dec. 3,850 350 Sum $ 51,767 6,260 Average $ 4,313.92 521.67 Average cost per hour ($51,767/6,260) = $8.27 (rounded to the nearest cent) r = 0.85977 r2 = 0.73920 The percent of the total variance that…
Demand for oil changes at Garcia's Garage has been as follows: Month Number of Oil Changes January 43 February 37 March 53 April 61 May 67 June 43 July 52 August 67 a. Use simple linear regression analysis to develop a forecasting model for monthly demand. In this application, the dependent variable, Y, is monthly demand and the independent variable, X, is the month. For January, let X=1; for February, let X=2; and so on. The forecasting model is given by the equation Y=...............+.............X. (Enter your responses rounded to two decimal places.)
Midgett Co. has accumulated data to use in preparing its annual profit plan for the upcoming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff suggested that linear regression be employed to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis are as follows: Month MaintenanceCost Machine Hours Jan. $ 5,040 620 Feb. 3,648 420 Mar. 4,320 520 Apr. 3,331 390 May 5,221 650 June 3,550 400 July 3,655 430 Aug. 5,365 690 Sept. 5,110 640 Oct. 4,866 610 Nov. 3,944 460 Dec. 3,790 440 Sum $ 51,840 6,270 Average $ 4,320.00 522.50 Average cost per hour ($51,840/6,270) = $8.27 (rounded to the nearest cent)r = 0.99821r2 = 0.99780The percent of the total variance that can be…
Assume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old?
If we collect monthly sales over two years for N=100 stores, we should not apply a simple linear regression model directly to the data, because the observations are not independent with each other. Is this statement True or False? A) True B) False
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.…
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 210 2,520 144 44,100 10 15.5 190 2,945 240.25 36,100 Total 151 1,750 2,312 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.627 3.173 2.877 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the…

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