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.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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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,
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.
Expert Solution
Step 1
In this case, the independent variable is hours of cycling (x) and the dependent variable is levels of stress (y).
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