With the below question, for the first part of the question, I did a scatterplot

Question

With the below question, for the first part of the question, I did a scatterplot (also below). I also performed a linear regression (image of result below). Do I need to do pearson correlation as well? And if so, how do I write up the results of the linear regression and pearson's correlation (results of the pearson's correlation are also below)?

For the second part of the question, how do I determine whether the relationship between BMI (continuous) and weekly minutes moderate exercise (continuous) differs between the age groups. I have a categorical age group called AgeGrpA that is categorised into "over 45" and "under 45".

Question:

Consider body mass index BMI (BMI_r_num) 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?

Please type answer (not hand write). Thanks!

Residuals: 1 Median Max Min 3Q -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

According to the above performed test, since in the Pearson product moment correlation test , the p value=0.000636 is less than 0.05,therefore our H0 that there is no significant difference 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 is rejected.

Therefore it is concluded that 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

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