Question

When evaluating a regression output the P-value will show which of the following?

(a). the empirical probability percent
(b).the correlation between the variablos used in the regreusion
(c).the percent probability that the relationshlp between the independent and dependent variable ls just a coincidence.
(d).the minimum predicted value
(e).the percent of the variation in the dependent variable that tan be explainad by variations in the independent variable.

Answer 1

The P-value in a regression output indicates the likelihood that the relationship between the independent and dependent variables is a coincidence, with a low P-value (typically < 0.05) suggesting a significant relationship.

Step-by-step explanation:

When evaluating a regression output, the P-value indicates the probability that the relationship between the independent and dependent variables is due to random chance. Specifically, it addresses (c) the percent probability that the relationship between the independent and dependent variable is just a coincidence. If the P-value is low, typically less than 0.05, we reject the null hypothesis that there is no linear relationship—indicating that it is unlikely the observed correlation is due to random chance.

In a regression analysis, the independent variable is the one manipulated or controlled by the researcher, while the dependent variable is what is being measured or predicted. The correlation coefficient (r) measures the strength of the linear relationship between the two variables, with the coefficient of determination (r²) explaining the percentage of variation in the dependent variable due to the independent variable.