I have used a multi-way ANOVA to answer the last part of the below question. Is

Question

I have used a multi-way ANOVA to answer the last part of the below question. Is that the right test? And if so, how do I write up my results? I included my results below the question. AgeGrpA is split into two categories: 45 and over, less than 45. BMI is a continuous variable. Weekly minutes of moderate exercise is a continuous variable.

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?

Anova Table (Type II tests) Response Weekly MinutesModerateExercise r Sum Sq Df F value Pr (>F) AgeGrpA r 375216 1 1.9683 0.16098 BMI r 1764976 3.0862 0.02656 Age GrpA r: BMI r 414964 3 0.7256 0.53682 169473086 889 Residuals Signif codes 0 0.001 0.01 0.05 0.1 1 with (Dataset (tapply (WeeklyMinutes ModerateExercise r, list (AgeGrpA r, BMI r), mean. na.rma TRUE))) t means healthy weight obese overweight underweight 45 and over 273.7853 137.1698 237.8465 168.75 less than 45 269.5000 248.5946 280.3425 126.00

Explanation / Answer

ANOVA test is of course right test.

According to the ANOVA table AgeGrpA_r and the interaction between AgeGrpA_r and BMI_r is not significance at 5 level.

So, the model reduced to only the general effect and the effect due to BMI_r. The reduced model is good predictive model.

BMI_r differs for both the age groups in each weights.

And the weekly minutes of moderate exercise hours differs for both the age groups in obese, overweight, underweight by mean & healthy weight, obese , underweight by standard deviation.

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