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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?A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). The Excel-generated Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833 Total 4 631.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 a. From the Excel-generated Regression output above, give the value of b0, the estimated y-intercept. Round off your answer to the fourth decimal place. b0 =____. b. From the Excel-generated Regression output above, give the value of b1 , the estimated slope. Round off your answer to the fourth decimal place. b1 = _________A Simple Linear Regression (SLR) was performed where the monthly Revenue ("Rev", the y-variable) was regressed on the monthly Advertising Expenditures ("Expend", the x-variable). The Excel-generated Regression output is provided below: ANOVA df SS MS F Significance F Regression 1 492.528125 492.528125 10.65525634 0.046980871 Residual 3 138.671875 46.22395833 Total 4 631.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 23.1328125 5.324310936 4.344752359 0.022510469 6.188478833 40.07714617 Expend 3.1015625 0.950164031 3.264239014 0.046980871 0.077716489 6.125408511 a. From the Excel-generated Regression output above, give the value of b subscript o, the estimated y-intercept. Round off your answer to the fourth decimal place. b subscript 0 = Blank 1. Fill in the blank, read surrounding text. b. From the Excel-generated Regression output above, give the value of b subscript 1, the estimated slope. Round off your answer to…
- The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of dollars. The summary output for the regression model is given below. ANOVA dfdf SSSS MSMS FF Significance FF Regression 1 19.52147562 19.52147562 19.03486740 0.002403282 Residual 8 8.204512367 1.02556405 Total 9 27.72598799 Step 2 of 3 : What is the adjusted coefficient of determination for this model, R2a? Round your answer to four decimal places.A part of the output of a regression analysis of Y against X using Excel is given below:SUMMARY OUTPUTRegression StatisticsMultiple R 0.954704R Square 0.91146Adjusted R Square 0.896703Standard Error 28.98954Observations 8ANOVAdf SS MS F Significance FRegression 1 51907.64 51907.64Residual 6 5042.361 840.3936Total 7 56950Coefficients Standard Error t Stat P-valueIntercept 45.2159 39.8049Age 5.3265 0.6777a. State the estimated regression line and interpret the 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…
- Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73720.7372 R Square 0.54340.5434 Adjusted R Square 0.52350.5235 Standard Error 2120.66062120.6606 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 246,191,336.3605246,191,336.3605 123,095,668.1803123,095,668.1803 27.371627.3716 1.5E-081.5E-08 Residual 4646 206,871,255.7619206,871,255.7619 4,497,201.21224,497,201.2122 Total 4848 453,062,592.1224453,062,592.1224 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14262.1701214262.17012 2,508.63812,508.6381 5.68525.6852 0.0000008560.000000856 9212.54359212.5435 19,311.796719,311.7967 Education (Years) 2354.97312354.9731 335.4472335.4472 7.02047.0204 0.0000000080.000000008 1679.75291679.7529 3030.19333030.1933 Experience (Years) 830.0759830.0759…Consider the following computer output of a multiple regression analysis relating annual salary to years of education and years of work experience. Regression Statistics Multiple R 0.73720.7372 R Square 0.54340.5434 Adjusted R Square 0.52350.5235 Standard Error 2120.66062120.6606 Observations 4949 ANOVA dfdf SSSS MSMS F� Significance F� Regression 22 246,191,336.3605246,191,336.3605 123,095,668.1803123,095,668.1803 27.371627.3716 1.5E-081.5E-08 Residual 4646 206,871,255.7619206,871,255.7619 4,497,201.21224,497,201.2122 Total 4848 453,062,592.1224453,062,592.1224 Coefficients Standard Error t� Stat P-value Lower 95%95% Upper 95%95% Intercept 14262.1701214262.17012 2,508.63812,508.6381 5.68525.6852 0.0000008560.000000856 9212.54359212.5435 19,311.796719,311.7967 Education (Years) 2354.97312354.9731 335.4472335.4472 7.02047.0204 0.0000000080.000000008 1679.75291679.7529 3030.19333030.1933 Experience (Years) 830.0759830.0759…The owner of a new pizzeria in town wants to study the relationship between weekly revenue and advertising expenditures. All measures are recorded in thousands of dollars. The summary output for the regression model is given below.ANOVA dfdf SSSS MSMS F� Significance F� Regression 11 16.8975147616.89751476 16.8975147616.89751476 16.9480751816.94807518 0.0062385580.006238558 Residual 66 5.9821004755.982100475 0.997016750.99701675 Total 77 22.8796152422.87961524 Step 2 of 3 : What is the adjusted coefficient of determination for this model, R2a��2? Round your answer to four decimal places.
- A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…Here there is a skewness and kurtosis test for residuals of a linear regression analysis. Interpret the values and histogram of residuals to check whether there is normal distribution. kurtosis n NADeveloped 0.349937 448 64Developing 3.469676 2010 416 kurtosis n NADeveloped 0.349937 448 64Developing 3.469676 2010 416The 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?
