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Table 8.1: Selected Excel output from a simple linear regression of levels of stress and average hours of cycling a week; n=80 ANOVA Significance F df S MS Regression 1 330.0887 330.0887 439.5926 8.61E-34 Residual 78 58.56994 0.750897 Total 79 388.6586 Standard Coefficients Error t Stat P-value Intercept Hours of cycling 8.174779154 0.201398 40.59015 <0.0001 (week) -0.151563181 0.007229 -20.9665 <0.0001 By looking at the output in Table 8.1, write down the equation of the fitted regression model, and explain the meaning of the regression coefficients in context. Comment on the statistical significance of the regression coefficients.

Table 8.1: Selected Excel output from a simple linear regression of levels of stress and average hours of cycling a week; n=80 ANOVA Significance F df S MS Regression 1 330.0887 330.0887 439.5926 8.61E-34 Residual 78 58.56994 0.750897 Total 79 388.6586 Standard Coefficients Error t Stat P-value Intercept Hours of cycling 8.174779154 0.201398 40.59015 <0.0001 (week) -0.151563181 0.007229 -20.9665 <0.0001 By looking at the output in Table 8.1, write down the equation of the fitted regression model, and explain the meaning of the regression coefficients in context. Comment on the statistical significance of the regression coefficients.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
Problem 8P
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The last part of Sloan's report concerns the connection between cycling and the level of stress. To investigate this link, Sloan first collected information about how many hours a week on average a sample of Kiloton bicycle owners go cycling. She then invited them to a lab where their level of stress was measured with a combination of tests that included heartrate monitoring and oxygen consumption measurement. With this measurement, the stress level can be as high as 10 and as low as 0. Sloan collected 80 responses. To understand her data better, she plotted the average hours of cycling per week against the level of stress on a scatter plot shown Figure 1 below. Sloan decides to fit a simple linear regression model to the data to investigate the relationship between stress levels and average time spent cycling. The fitted regression line has been superimposed on the scatter plot in Figure 8.1. Table 8.1 shows the selected outputs from the regression analysis. Figure 8.1: Stress levels against hours of cycling with fitted regression line superimposed on the plot. Scatterplot of levels of stress and hours cycling a week 10 8. 7 6 4 3 1 10 20 30 40 50 60 Average hours of cycling (week) Level of stress 9,
Transcribed Image Text:The last part of Sloan's report concerns the connection between cycling and the level of stress. To investigate this link, Sloan first collected information about how many hours a week on average a sample of Kiloton bicycle owners go cycling. She then invited them to a lab where their level of stress was measured with a combination of tests that included heartrate monitoring and oxygen consumption measurement. With this measurement, the stress level can be as high as 10 and as low as 0. Sloan collected 80 responses. To understand her data better, she plotted the average hours of cycling per week against the level of stress on a scatter plot shown Figure 1 below. Sloan decides to fit a simple linear regression model to the data to investigate the relationship between stress levels and average time spent cycling. The fitted regression line has been superimposed on the scatter plot in Figure 8.1. Table 8.1 shows the selected outputs from the regression analysis. Figure 8.1: Stress levels against hours of cycling with fitted regression line superimposed on the plot. Scatterplot of levels of stress and hours cycling a week 10 8. 7 6 4 3 1 10 20 30 40 50 60 Average hours of cycling (week) Level of stress 9,
Table 8.1: Selected Excel output from a simple linear regression of levels of stress and average hours of cycling a week; n=80 ANOVA Significance df MS F Regression 1. 330.0887 330.0887 439.5926 8.61E-34 Residual 78 58.56994 0.750897 Total 79 388.6586 Standard Coefficients Error t Stat P-value Intercept Hours of cycling 8.174779154 0.201398 40.59015 <0.0001 (week) -0.151563181 0.007229 -20.9665 <0.0001 By looking at the output in Table 8.1, write down the equation of the fitted regression model, and explain the meaning of the regression coefficients in context. Comment on the statistical significance of the regression coefficients.
Transcribed Image Text:Table 8.1: Selected Excel output from a simple linear regression of levels of stress and average hours of cycling a week; n=80 ANOVA Significance df MS F Regression 1. 330.0887 330.0887 439.5926 8.61E-34 Residual 78 58.56994 0.750897 Total 79 388.6586 Standard Coefficients Error t Stat P-value Intercept Hours of cycling 8.174779154 0.201398 40.59015 <0.0001 (week) -0.151563181 0.007229 -20.9665 <0.0001 By looking at the output in Table 8.1, write down the equation of the fitted regression model, and explain the meaning of the regression coefficients in context. Comment on the statistical significance of the regression coefficients.
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