what is the level of statistical significance for the intercept coefficient (a)
ID: 3153873 • Letter: W
Question
what is the level of statistical significance 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.
Please estimate the following linear regression model on this dataset:
Y = a + b X
When selecting the significance level of a coefficient, you need to determine the lowest value at which the test will start to fail to reject the null hypothesis (the coefficient is equal to zero).
Example: Recall that when you have a P-value of 0.03, that implies that hypothesis tests with significance levels above 0.97 will fail to reject the null, while tests with significance levels below 0.97 will fail to reject the null.
SUMMARY OUTPUT Regression Statistics Multiple R 0.96809142 R Square 0.93720099 Adjusted R Square 0.93495817 Standard Error 17.7612116 Observations 30 ANOVA df SS MS F Significance F Regression 1 131820.569 131820.569 417.866931 2.2853E-18 Residual 28 8832.89786 315.460638 Total 29 140653.467 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.63001251 9.95981731 0.56527267 0.57639013 -14.771748 26.0317734 -14.771748 26.0317734 X Variable 1 3.03473443 0.14845735 20.4417937 2.2853E-18 2.73063335 3.33883552 2.73063335 3.33883552Explanation / Answer
what is the level of statistical significance 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.
This question refers to the P value. From the data table, the P value of the slope (under X Variable 1) is
P = critical significance = 2.2853*10^-18 [ANSWER]
[Note: The "Example" has mistaken the "confidence level" to the "significance level". Significance levels are always closer to 0 than 1, but it said 0.97 is the significance level. 0.03 is actually the critical level of significance.
Note of the relationship
significance = 1 - confidence.]
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Please estimate the following linear regression model on this dataset:
Y = a + b X
From the table, we have the "coefficients",
Y = 5.63001251 + 3.03473443X [ANSWER]
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