ANOVAs table for partial regression model.
Information is presented on the relationships of systolic blood pressure (dependant variable, in mmHg) to age (X_{1}, in years), weight (X_{2}, coded 1 for overweight, 0 for normal), physical activity level (X_{3}, coded 1 for active, 0 for sedentary) and smoking history (X_{4}, coded 1 for current or exsmoker, 0 for never smoked) among 259 subjects. An abbreviated ANOVA table based on the regression of systolic blood pressure on all four independent variables is shown below:
Source

DF

SS

X_{1}

1

7146.40

X_{2}  X_{1}

1

1750.73

X_{3}  X_{1}, X_{2}

1

667.26

X_{4}  X_{1}, X_{2}, X_{3}

1

406.05

Residual

245

73581.52

a) Can you test the significance of the relationship between physical activity level and systolic blood pressure, adjusting for age, weight, and smoking history, given ANOVA table above? If so, carry out the test and interpret the result. If not, how must the variables is ordered so that the test can be performed?
b) Can you test the significance of the relationship between physical activity level and systolic blood pressure, adjusting for age, and weight, given the ANOVA table above? If so, carry out the test and interpret the result. If not, how ought the variables is ordered so that the test can be performed?