Question

A doctor wanted to determine whether there is a relation between a male’s age and his HDL (so-called good cholesterol). He randomly selected 9 of his patients and determined their HDL cholesterol. The data is reported in the table below: Age (Yrs) HDL (LaTeX: \mu μ mol/L)

38 57

42 54

46 34

32 56

55 35

52 40

61 42

61 38

26 47

a) Compute the regression equation for HDL as a function of age.

b)Interpret the meaning of the regression parameters.

c) Compute r and r2. Interpret these statistics.

d) What is your opinion of the usefulness of using age as a predictor of HDL?

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.661532
R Square	0.437624
Adjusted R Square	0.357285
Standard Error	7.246119
Observations	9
ANOVA
	df	SS	MS	F	Significance F
Regression	1	286.0118	286.0118	5.447197	0.052311
Residual	7	367.5437	52.50625
Total	8	653.5556
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	66.79099	9.736212	6.860059	0.00024	43.76851	89.81347	43.76851	89.81347
Age	-0.47971	0.205537	-2.33392	0.052311	-0.96572	0.00631	-0.96572	0.00631

a.) HDL = 66.79099 - 0.47971 * Age

b.) The coefficient of age can be interpreted as increase in HDL on 1 year increase in age

c.) Correlation coefficient (r) = 0.661532 and R² = 0.437624.

So about 43.76% of the variation in HDL is explained by the variation in age

d.) The model R² is not very high and also the coefficient of age is not significant at 5% level of significance. Thus age may not be a useful predictor of HDL