Question

Use Minitab, R, or your preferred software for this question.

An exercise physiologist used skinfold measurements to estimate the total body fat, Y, expressed as a percentage of body weight, X₁, for 19 participants in a physical fitness program. Body fat percentage and body weight are shown in the table below.

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
Weight (kg)	89	88	66	59	93	73	82	77	100	67	57	68	69	59	62	59	56	66	72
Body Fat (%)	28	27	24	23	29	25	29	25	30	23	29	32	35	31	29	26	28	33	23

Note that participants 1-10 are male and 11-19 are female. Define a variable X₂ which is 1 for males and 0 for females, and fit the model Y=β₀+β₁X₁+β₂X₂+e.

What is the estimated value of the regression coefficient for variable Weight?  [2 pt(s)]

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What is the estimated value of the intercept?  [2 pt(s)]

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What is your computed value of SSE?  [2 pt(s)]

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What is your computed value of MSE?  [1 pt(s)]

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What is the standard error of the estimate of β₁?  [2 pt(s)]

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Answer 1

applying multiple regression on above data:

1)estimated value of the regression coefficient for variable Weight=0.169028

2) estimated value of the intercept =18.887980

3) computed value of SSE =117.544016

4)computed value of MSE =7.346501

5)standard error of the estimate of β_{1 =} 0.063063