An observational study was conducted where subjects were randomly sampled and then had their resting heart rate recorded, as well as their smoking status (0 for non-smoker and 1 for smoker) and how much they exercise on average each day (in hours). A linear regression model is fit where we have response variable of resting heart rate and explanatory variables of smoking status (0 for non-smoker and 1 for smoker) and exercise amount per day in hours, along with an interaction between smoking status and exercise amount. The output is below: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 84.8172 1.9553 43.377 <2e-16 *** Smoke -2.2645 5.0665 -0.447 0.6551 Exercise -7.3684 0.8075 -9.125 <2e-16 *** Smoke: Exercise 1.9562 2.5510 0.767 0.4442 Signif. codes: O **** 0.001 **** 0.01 *** 0.05 .' 0.1 Residual standard error: 8.396 on 228 degrees of freedom Multiple R-squared: 0.2971, F-statistic: 32.13 on 3 and 228 DF, Adjusted R-squared: p-value: < 2.2e-16 0.2879 The model that was fit is: Rest; = Bo + B Smoke; + B2 Eercise; + B3Smoke; * Exercise; + €;

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Calculate a 95% confidence interval for the effect of a one unit increase in exercise on resting
heart rate for a non-smoker (Smoke=0). That is, creat a 95% confidence interval for B2. Use 1.96
as the 95% multiplier.
What is the lower limit of this 95% confidence interval?
Transcribed Image Text:Calculate a 95% confidence interval for the effect of a one unit increase in exercise on resting heart rate for a non-smoker (Smoke=0). That is, creat a 95% confidence interval for B2. Use 1.96 as the 95% multiplier. What is the lower limit of this 95% confidence interval?
An observational study was conducted where subjects were randomly sampled and then had
their resting heart rate recorded, as well as their smoking status (0 for non-smoker and 1 for
smoker) and how much they exercise on average each day (in hours).
A linear regression model is fit where we have response variable of resting heart rate and
explanatory variables of smoking status (0 for non-smoker and 1 for smoker) and exercise
amount per day in hours, along with an interaction between smoking status and exercise
amount.
The output is below:
Coefficients:
Estimate Std. Error t value Pr(>t)
(Intercept)
84.8172
1.9553
43.377
<2e-16 ***
Smoke
-2.2645
5.0665
-0.447
0.6551
Exercise
-7.3684
0.8075
-9.125
<2e-16 ***
Smoke: Exercise
1.9562
2.5510
0.767
0.4442
Signif. codes:
O **** 0.001 (*** 0.01 *' 0.05 .' 0.1 '
1
Residual standard error: 8.396 on 228 degrees of freedom
Adjusted R-squared:
Multiple R-squared: 0.2971,
F-statistic: 32.13 on 3 and 228 DF, p-value: < 2.2e-16
0.2879
The model that was fit is:
Rest; = Bo + B, Smoke; + B2Exercise; + B3 Smoke; * Exercise; + e;
Transcribed Image Text:An observational study was conducted where subjects were randomly sampled and then had their resting heart rate recorded, as well as their smoking status (0 for non-smoker and 1 for smoker) and how much they exercise on average each day (in hours). A linear regression model is fit where we have response variable of resting heart rate and explanatory variables of smoking status (0 for non-smoker and 1 for smoker) and exercise amount per day in hours, along with an interaction between smoking status and exercise amount. The output is below: Coefficients: Estimate Std. Error t value Pr(>t) (Intercept) 84.8172 1.9553 43.377 <2e-16 *** Smoke -2.2645 5.0665 -0.447 0.6551 Exercise -7.3684 0.8075 -9.125 <2e-16 *** Smoke: Exercise 1.9562 2.5510 0.767 0.4442 Signif. codes: O **** 0.001 (*** 0.01 *' 0.05 .' 0.1 ' 1 Residual standard error: 8.396 on 228 degrees of freedom Adjusted R-squared: Multiple R-squared: 0.2971, F-statistic: 32.13 on 3 and 228 DF, p-value: < 2.2e-16 0.2879 The model that was fit is: Rest; = Bo + B, Smoke; + B2Exercise; + B3 Smoke; * Exercise; + e;
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