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: 0.2879 F-statistic: 32.13 on 3 and 228 DF, p-value: < 2.2e-16 Multiple R-squared: 0.2971, The model that was fit is: Rest; = Bo + B1 Smoke; + B2Exercise; + B3Smoke; * Exercise; + E;

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: 0.2879 F-statistic: 32.13 on 3 and 228 DF, p-value: < 2.2e-16 Multiple R-squared: 0.2971, The model that was fit is: Rest; = Bo + B1 Smoke; + B2Exercise; + B3Smoke; Exercise; + E;

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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