A coefficient test fails to reject H0:beta=0 at the chosen alpha under the stated regression assumptions. What follows?
Correct Answer
C) There is insufficient evidence against the zero-coefficient null at that alpha
Under the specified test and assumptions, failure to reject H0:beta=0 means the data do not provide sufficient evidence against that null at the chosen alpha. It does not prove an exactly zero or immaterial effect. Low precision, correlated predictors or limited information may contribute. Do not double the coefficient or discard the whole model automatically; investigate its role and uncertainty.
Why This Is the Correct Answer
Option C is correct because failing to reject H0: beta = 0 at the chosen alpha means there is insufficient evidence against the zero-coefficient null. Low precision, correlated predictors or limited data may contribute, so the appraiser should investigate the variable's role and uncertainty rather than treat the effect as proven zero.
Why the Other Options Are Wrong
Option A: The test proves the feature has exactly zero market effect in each comparable sale analyzed
Option A, that the test proves the feature has exactly zero market effect in each comparable sale, overstates the result. Absence of evidence against the null is not proof that the effect is zero, and the test concerns a population parameter, not each sale.
Option B: The entire regression must be discarded
Option B, that the entire regression must be discarded, does not follow. One insignificant coefficient calls for investigating that variable's role, not automatically abandoning the whole model.
Option D: The coefficient should be doubled
Option D, that the coefficient should be doubled, has no statistical basis. A test outcome does not justify arbitrarily rescaling a coefficient.
Not proven is not disproven
Failing to reject zero means the case against zero was not proven, not that zero was proven. The effect might still exist.
How to use: Use this to reject choices that treat a non-significant result as proof of no effect.
Exam Tip
Pick the answer phrased as insufficient evidence; reject choices claiming proof of zero effect or drastic actions on the model.
Common Mistakes to Avoid
- -Treating failure to reject as proof of zero effect
- -Discarding the whole model because one coefficient is not significant
- -Ignoring correlated predictors as a cause of imprecision
Concept Deep Dive
Analysis
This question tests interpreting a failure to reject the null hypothesis for a regression coefficient. Failing to reject H0: beta = 0 means the data do not provide enough evidence against a zero coefficient at that alpha; it does not prove the effect is zero.
Background Knowledge
In hypothesis testing, failing to reject the null means the evidence is not strong enough to rule it out at the chosen alpha. For regression coefficients, this can occur when the true effect is small, the data are limited or predictors are correlated. Appraisers interpret such results cautiously and consider uncertainty and market evidence.
Real-World Application
An appraiser's regression shows a fireplace coefficient that is not statistically significant. Rather than concluding fireplaces add nothing, the appraiser notes the small number of sales with fireplaces and looks at paired sales for more evidence.
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