Question

Skinfold	Thigh	Midarm	Body Fat
19.5	43.1	29.1	11.9
24.7	49.8	28.2	22.8
30.7	51.9	37	18.7
29.8	54.3	31.1	20.1
19.1	42.2	30.9	12.9
25.6	53.9	23.7	21.7
31.4	58.5	27.6	27.1
27.9	52.1	30.6	25.4
22.1	49.9	23.2	21.3
25.5	53.5	24.8	19.3
31.1	56.6	30	25.4
30.4	56.7	28.3	27.2
18.7	46.5	23	11.7
19.7	44.2	28.6	17.8
14.6	42.7	21.3	12.8

Run a multiple regression (in Excel) with body fat as the dependent variable and skinfold, midarm and thigh as independent variables. Show the results. Comment on the predictive value of the results.

Answer 1

The results are:

The regression model is:

y = 175.2317 + 6.0768*x1 - 4.3310*x2 - 3.1430*x3

The hypothesis being tested is:

H₀: β₁ = β₂ = β₃ = 0

H₁: At least one β_i ≠ 0

The p-value is 0.0003.

Since the p-value (0.0003) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

Since the model is significant, the model is accurate and can be used for predictions.