A study was conducted to see whether heart rate (y) on swimmers linearly related to their age (x1) and swimming time for 2000 meters (x2). A random sample of ten swimmers was selected and the result is shown in the following Microsoft Excel output. (a) Interpret the value of R2 from the output.         (b) Conduct a hypothesis test to test whether the linear regression model is fit or not using a = 0.05.         (c) Calculate the 95% confidence interval for the coefficient value for age

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Section4.6: Applications And The Perron-frobenius Theorem
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A study was conducted to see whether heart rate (y) on swimmers linearly related to their age (x1) and swimming time for 2000 meters (x2). A random sample of ten swimmers was selected and the result is shown in the following Microsoft Excel output.

(a) Interpret the value of R2 from the output.
     
  (b) Conduct a hypothesis test to test whether the linear regression model is fit or not using a = 0.05.
     
  (c) Calculate the 95% confidence interval for the coefficient value for age.
     
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R
Square
Standard Error
Observations
ANOVA
Regression
Residual
Total
Intercept
Age
Swim Time
0.19
0.04
-0.24
10.60
10
df
2
7
9
Coefficients
226.15
-0.62
-2.03
SS
30.45
785.95
816.40
Standard
Error
176.92
1.56
4.68
MS
15.22
112.28
t Stat
1.28
-0.40
-0.43
Transcribed Image Text:SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Intercept Age Swim Time 0.19 0.04 -0.24 10.60 10 df 2 7 9 Coefficients 226.15 -0.62 -2.03 SS 30.45 785.95 816.40 Standard Error 176.92 1.56 4.68 MS 15.22 112.28 t Stat 1.28 -0.40 -0.43
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