Consider the following data for a dependent variable y and two independent variables, X1 and X2. X1 X2 y 30 12 92 47 10 108 25 17 112 51 16 178 40 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 212 The estimated regression equation for these data is = -20.08 + 2.04x, + 4.77x2' Here, SST = 15,514.0, SSR = 14,359.4, sp. = 0.2497, and Sp. = 0.9584. %3D

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Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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Consider the following data for a dependent variable y and two independent variables, x,
and x2.
X1 X2 y
30
12
92
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
212
The estimated regression equation for these data is
ŷ = -20.08 + 2.04x, + 4.77x2'
%D
Here, SST =
15,514.0, SSR
14,359.4, Sb1
= 0.2497,
= 0.9584.
and
Transcribed Image Text:Consider the following data for a dependent variable y and two independent variables, x, and x2. X1 X2 y 30 12 92 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 16 212 The estimated regression equation for these data is ŷ = -20.08 + 2.04x, + 4.77x2' %D Here, SST = 15,514.0, SSR 14,359.4, Sb1 = 0.2497, = 0.9584. and
(c) Is B, significant? Use a = 0.05.
State the null and alternative hypotheses.
Ho: B2
Ha: B2 > 0
Ho: B2 < 0
H3: B2 2 0
O Ho: B2 > 0
Ha: B2s 0
O Ho: B2 # 0
Ha: B2
O Ho: B2 = 0
Ha: B2 # 0
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to three decimal places.)
p-value
State your conclusion.
Do not reject Ho: There is sufficient evidence to conclude that B, is significant.
Do not reject Ho. There is insufficient evidence to conclude that B, is significant.
Reject Ho. There is sufficient evidence to conclude that ß, is significant.
Reject Ho. There is insufficient evidence to conclude that ß, is significant.
Transcribed Image Text:(c) Is B, significant? Use a = 0.05. State the null and alternative hypotheses. Ho: B2 Ha: B2 > 0 Ho: B2 < 0 H3: B2 2 0 O Ho: B2 > 0 Ha: B2s 0 O Ho: B2 # 0 Ha: B2 O Ho: B2 = 0 Ha: B2 # 0 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value State your conclusion. Do not reject Ho: There is sufficient evidence to conclude that B, is significant. Do not reject Ho. There is insufficient evidence to conclude that B, is significant. Reject Ho. There is sufficient evidence to conclude that ß, is significant. Reject Ho. There is insufficient evidence to conclude that ß, is significant.
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