e-Statistics

## Inference on Two Variables

The multiple linear regression model

are identified with the following variables:
1. Response (dependent variable) for 's;
2. 1st predictor (1st explanatory variable) for 's;
3. 2nd predictor (2nd explanatory variable) for 's.

The standard error for the estimate gives rise to the null hypothesis

for . It can be constructed to find whether the response is dependent of the i-th predictor. Under the null hypothesis the test statistic is distributed as the t-distribution with degrees of freedom. Thus, we reject at significance level if . By computing the p-value we can equivalently reject if .