Question

Q12: The following data are from a study of the relationship between average consumption of saturated fat (in grams) and cholesterol level (in milligram per hundred milliliters) of eight males:

Subject	1	2	3	4	5	6	7	8
Fat consumption (x)	55	65	50	34	43	58	72	36
Cholesterol level (y)	180	215	195	165	170	204	235	150

Below are some of the summaries of this data:

∑?=413, ∑?=1514, ????=1277.875, ????=5591.5 and ????=2536.75

(a) Compute the estimates of regression coefficients β0 and β1 and write the fitted regression line.

(b) Does the amount of fat consumption determine the cholesterol level? Carry out a hypothesis test to support your answer at 2% significance level.

(c) Construct a 98% confidence interval for β1.

(d) Calculate the variability in the cholesterol level not explained by the amount of fat consumption and interpret it.

Answer 1

Above problem is solved using Minitab, output of Minitab is attached below

a) Beta 0 = 86.8, Beta 1 = 1.985

Regression line,

Yhat = 86.8 + 1.985 * X

b) Ho: Beta 1 = 0 vs H1: Beta 1 ≠ 0

P value = 0.00 > alpha = 0.02

Ho is rejected.

Therefore, the amount of fat consumption determine the cholesterol level

c) 98 % CI,

( 1.139,2.831)

d) 1- R2 = 1- 0.9006 = 0.0994 = 9.94 %

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