The accompanying table shows the regression results when estimating y = β_{0} + β_{1}x_{1} + β_{2}x_{2} + β_{3}x_{3} + ε.
df | SS | MS | F | Significance F | |
Regression | 3 | 453 | 151 | 5.03 | 0.0030 |
Residual | 85 | 2,521 | 30 | ||
Total | 88 | 2,974 | |||
Coefficients | Standard Error | t-stat | p-value | ||
Intercept | 14.96 | 3.08 | 4.80 | 0.0000 | |
x_{1} | 0.87 | 0.29 | 3.00 | 0.0035 | |
x_{2} | 0.46 | 0.22 | 2.09 | 0.0400 | |
x_{3} | 0.04 | 0.34 | 0.12 | 0.9066 |
At the 5% significance level, which of the following explanatory
variable(s) is(are) individually significant?
Multiple Choice:
Only x_{1}
Only x_{3}
x_{1} and x_{2}
x_{2} and x_{3}
Solution:
If the p-value is less than value, then it is statistically significant.
Given the value of =5%=0.05
Let us check the above condition to find the result.
p-value | Comparison | Result | |
x_{1} | 0.0035 | 0.0035<0.05 | Significant |
x_{2} | 0.04 | 0.04<0.05 | Significant |
x_{3} | 0.9066 | 0.9066>0.05 | Not significant |
From the above table we can see that the explanatory variables x_{1} and x_{2} is significant because its p-value is less than value.
So option 3 is the correct answer.
x_{1} and x_{2}
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