Question

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.01α=0.01.

X1X1	X2X2	YY
23.5	33.6	50.2
8.7	31.6	53.7
24.3	43	43
16.7	24.6	83.6
34.2	39.1	45
52.2	30	55.4
32.7	41.8	34.2
24.8	20.6	71.7
31.8	44.1	51.3
46.7	52.7	17.4
19.5	23.4	81.6
18.7	46.2	48.2
52.1	47.3	54.3
34.1	6.7	81.7
64.6	36.7	41.3
63.4	57.5	17.8
83.1	44.7	31.5
44.3	27.8	43.8
56.8	42.4	22.7
55.9	49.1	37.3

SSreg=SSreg=
SSres=SSres=
R2=R2=
F=F=
P-value =

What is your decision for the hypothesis test?

• Reject the null hypothesis, H0:β1=β2=0H0:β1=β2=0
• Fail to reject H0H0

What is your final conclusion?

• The evidence supports the claim that one or more of the regression coefficients is non-zero
• The evidence supports the claim that all of the regression coefficients are zero
• There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
• There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero

Answer 1