The table below contains 30 observations, each containing Y and X values. Please
ID: 3262665 • Letter: T
Question
The table below contains 30 observations, each containing Y and X values. Please estimate the following linear regression model on this dataset:
Y = a + b X
In this estimation, what is the level of statistical confidence for the intercept coefficient (a) to be different from zero? I.e., the level of significance above which, the test where the null hypothesis is that the coefficient (intercept) is equal to zero, fails to reject the null.
Y
X
161
46
205
63
301
97
115
30
251
81
89
25
290
94
159
52
46
21
259
88
212
64
301
98
174
54
149
42
130
42
249
79
297
95
229
66
109
59
129
47
212
65
200
67
180
57
303
97
231
73
225
71
138
42
138
42
270
86
192
60
a) 0.42361
b) 0.57693
c) 0.5653
d) 5.630
Y
X
161
46
205
63
301
97
115
30
251
81
89
25
290
94
159
52
46
21
259
88
212
64
301
98
174
54
149
42
130
42
249
79
297
95
229
66
109
59
129
47
212
65
200
67
180
57
303
97
231
73
225
71
138
42
138
42
270
86
192
60
Explanation / Answer
The regression equation is
Y = 5.63 + 3.03 X
Predictor Coef SE Coef T P
Constant 5.6300 9.9600 0.57 0.576
X 3.0347 0.1485 20.44 0.000
S = 17.7612 R-Sq = 93.7% R-Sq(adj) = 93.5%
From the list the correct answer for the estimate value of intercept is d) 5.630.
In this estimation, the common level of statistical confidence for the intercept coefficient (a) to be different from zero is 0.05. But, in this estimation, the estimated p-value is 0.576 and larger than 0.05 level of significance. Hence, we can not reject the null hypothesis and conclude that the value of intercept is not different from zero.
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