Final answer:
A strong relationship between a predictor and the response leads to a small p-value, often less than 0.05, indicating a statistically significant relationship and providing grounds to reject the null hypothesis of no relationship.
Step-by-step explanation:
When there is a strong relationship between a predictor and the response, the p-value associated with this relationship is expected to be small. A small p-value indicates that the observed relationship in the sample data is unlikely to have occurred by random chance if there was no actual relationship in the population (i.e., the null hypothesis is true).
For instance, if we have a sample correlation coefficient (r) that is far from zero and significant based on a hypothesis test, we are likely to get a small p-value. For example, a p-value of 0.026 is less than the commonly used significance level of 0.05. This would lead us to reject the null hypothesis that there is no relationship, suggesting that a significant linear relationship exists between the two variables being studied.
Therefore, in practice, if a strong relationship is indicated and the p-value is smaller than 0.05, or especially if it's less than 0.01, we would conclude that there is a statistically significant relationship between the predictor and the response.