The dataset below contains two variables (X and Y). Please estimate the following regression model:
Y = a + bX
Which of the coefficients (a and b in the equation above) are (is) statistically significant at 90% or higher confidence level?
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 |
Question 5 options:
a |
|
a and b |
|
b |
|
none |
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 4.6779286 + 3.0303126 X
Sample size: 23
R (correlation coefficient) = 0.96147942
R-sq = 0.92444267
Estimate of error standard deviation: 20.3318
Parameter estimates:
Parameter | Estimate | Std. Err. | Alternative | DF | T-Stat | P-value |
---|---|---|---|---|---|---|
Intercept | 4.6779286 | 12.510615 | ? 0 | 21 | 0.37391677 | 0.7122 |
Slope | 3.0303126 | 0.18904974 | ? 0 | 21 | 16.029182 | <0.0001 |
Analysis of variance table for regression
model:
Source | DF | SS | MS | F-stat | P-value |
---|---|---|---|---|---|
Model | 1 | 106212.19 | 106212.19 | 256.93466 | <0.0001 |
Error | 21 | 8681.0243 | 413.38211 | ||
Total | 22 | 114893.22 |
From the given table of p - values,
p - value for intercept = 0.7122
p - value for slope = 0.0000
Hence,
Only b is significant.
Option C is correct.
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