I have performed linear regression and pearson\'s correlation test for the below

Question

I have performed linear regression and pearson's correlation test for the below question first for BMI and WeeklyMinutesModerateExercise. Then I subset the data and did the same for under 45 and over 45.

How do I interpret the y=a+b*x for each linear regression? I assume I need to say something like "for every unit (not sure what unit to use) increase in excercise, BMI decreases by x.xx units"

I included a copy of each linear regression below as well. Please type the response. Thanks!

Question:

Consider body mass index BMI (BMI) as a continuous variable. Use weekly minutes of moderate exercise hours (WeeklyMinutesModerateExercise) in minutes per week as a continuous variable to predict BMI. Do you think this will provide a good predictive model? Also, does the relationship between BMI and weekly minutes of moderate exercise hours differ between those people under the age of 45 and greater than or equal to 45 years old?

Linear regression for the two variables:

linear regression for those under 45:

Residuals: 1 Median Min 3Q Max -15. 177 4.326 1.085 3.106 40.423 Coefficients Estimate Std. Error t value Pr (>lt I) (Intercept) 28.6767537 0.2374252 120.782 16 WeeklyMinutes ModerateExercise r 0.0016322 0.0004762 3.427 0.000636 Signif codes 0 0.001 0.01 0.05 0.1 1 Residual standard error: 6.448 on 932 degrees of freedom. (66 observations deleted due to missingness) Multiple R-squared 0.01245, Adjusted R-squared 0.01139 F-statistic: 11.75 on 1 and 932 DF, p-value 0.000636

Explanation / Answer

BMI = 28.6768 - 0.0016WeeklyMinutesExercise, For every 1 weekly minute increase in exercise the BMI decreases by 0.0016 Unit.

This is not a good predictive model as the adjusted R squared value is only 0.01139 = 1.139%. This means only 1.139% of the variance in the data is explained by this model.

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