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Use alpha = .05 for all inference on this assignment.
1. Using a sample of 108 people, we want to model total cholesterol, based on three independent variables: age, percent body fat, and BMI. We first obtained correlations among all pairs of variables. Next, we ran two regression models – one that contained all three independent variables, and another that contained only age and percent body fat.
i) With which variable(s) is total cholesterol related, looking at the correlations? Justify your answers by citing p - values.
Total Cholesterol is correlated with Age, PctBodyFat and BMI because p-values of these variables are smaller than 0.0001 at 5% level of significance.
ii) Interpret the R2 for the first regression model.
The value of R2 in the first regression model is 0.2493. It means that 24.93% of the variation in the dependent variable is explained by this model.
iii) Give the test statistic and interpret the overall F-test for the first regression model.
The test statistic value is 11.51 and the p-value associated with this model is smaller than 0.0001. We can see that the p-value is smaller than 0.05, it means that the model is significant at 5% level of significance....
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