(SA 1) Consider the relationship between weekly\_exercise\_hours (hours of exercise per week) and resting\_heart\_rate (resting heart rate in beats per minute). These variables are related because an increase in weekly exercise is generally associated with a decrease in resting heart rate. Answer the questions below using the following information: summary(weekly\_exercise\_hours) Min. 1st Qu. Median Mean 3rd Qu. Max. 0.0 2.0 4.0 5.0 8.0 10.0 $s^2 = 8.25$ summary(resting\_heart\_rate) Min. 1st Qu. Median Mean 3rd Qu. Max. 50.0 55.0 60.0 62.5 68.0 75.0 $s^2 = 25.0$ Partial R Output (from simple linear regression analysis): Coefficients: Estimate Std. Error (Intercept) 70.0 2.5 weekly\_exercise\_hours -1.5 0.4 ANOVA Table: Df Sum Sq Mean Sq F value Pr(>F) Regression 1 180.0 180.0 25.0 0.0005 Residuals 8 57.6 7.2 1. Specify the response and explanatory variables and write the regression equation. 2. Find and interpret the value of $R^2$.
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The regression equation is given by: $resting\_heart\_rate = \beta_0 + \beta_1 \times weekly\_exercise\_hours$ From the coefficients table, we have: $\beta_0 = 70.0$ (intercept) $\beta_1 = -1.5$ (slope) Therefore, the regression equation is: $resting\_heart\_rate Show more…
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