So how exactly is the p-value found? For simple regression, the p-value is determined using a t distribution with n − 2 degrees of freedom (df), which is written as \(t_{n−2}\), and is calculated as 2 × area past |t| under a \(t_{n−2}\) curve. In this example, df = 30 − 2 = 28.

The P-value The statistical test for this is called Hypothesis testing. A low P-value (< 0.05) means that the coefficient is likely not to equal zero. A high P-value (> 0.05) means that we cannot conclude that the explanatory variable affects the dependent variable (here: if Average_Pulse affects Calorie_Burnage).

A low p-value (< 0.05) indicates that you can reject the null hypothesis. In other words, a predictor that has a low p-value is likely to be a meaningful addition to your model because changes in the predictor's value are related to changes in the response variable.

For each test, the t-value is a way to quantify the difference between the population means and the p-value is the probability of obtaining a t-value with an absolute value at least as large as the one we actually observed in the sample data if the null hypothesis is actually true.