Question

A researcher would like to predict the dependent variable Y from the two independent variables X1 and X2 for a sample of N=12 subjects. Using multiple linear regression, it has been confirmed that the overall regression model is statistically significant at α=0.05 with F(2,9)=5.66 (p=0.026). Calculate the 95% confidence intervals for both partial slopes.

X1	X2	Y
66.2	60.5	75.2
41.6	19.3	26.9
52.5	57.2	50.4
60.9	42.5	44
75.2	49.3	71.6
63.9	57	56.5
36.8	62	45.6
38.5	61.4	68.1
42.9	50.3	55.4
64.7	56.1	48
48.1	38.7	48.6
45	56.9	49.4

critical value tα=2.26
Note: This value refers to the slopes and not the overall model significance.

b1=0.4
s(b1)=0.23
___ <β1< ___
HINT:
LL for CI for β_i = b_i - t_α * s(b_i)
UL for CI for β_i = b_i + t_α * s(b_i)

b2=0.65
s(b2)=0.24
___ <β2< ___

Which partial slopes are statistically significantly not equal to zero?

• neither
• b1
• b2
• both

Answer 1

The above solution is correct with full explanation. So please rate me high.