A predictor in linear regression with a p-value near zero is considered to have a significant coefficient.

• A. Not always
• B. True
• C. It depends on sample size
• D. False

Answer: (B)

In regression, we test whether a coefficient is zero by looking at its p-value. The p-value represents the probability, under the assumption that the true coefficient is zero, of observing data as extreme as what we actually saw. A p-value near zero means the observed relationship is highly unlikely under zero influence, which provides strong evidence that the coefficient is not zero. At standard significance levels (like 0.05 or 0.01), this leads to declaring the coefficient significant. So a p-value near zero is the hallmark of a significant predictor.

Keep in mind that significance is about the likelihood, not how large the effect is. Very large samples can produce tiny p-values for tiny effects, and small samples can fail to reach significance even with a meaningful effect. But with a p-value near zero, the coefficient is considered statistically significant.