Question

Consider the following data for a dependent variable y and two independent variables,  x₁ and x₂.

x1	x2	y
30	12	94
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	211

The estimated regression equation for these data isŷ = −18.37 + 2.01x₁ + 4.74x₂.

Here, SST = 15,182.9, SSR = 14,052.2, s_b1 = 0.2471,  and  s_b2 = 0.9484.

(A) Test for a significant relationship among x₁, x₂, and y. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

(b) Is β₁  significant? Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

(c) Is β₂  significant? Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

Answer 1

a)

p=number of independent variables=				2
MSR =SSR/p =		7026.100
MSE=(SSE/(n-p-1))=		161.529

F test statistic =MSR/MSE=			43.50
p value =	0.0001	or p value <0.01

b)

t test statistic =coefficient/standard error =					8.13
p value =	0.0001	or p value <0.01

c)

t test statistic =coefficient/standard error =					5.00
p value =	0.0016	or p value <0.01