Hypothesis testing in simple regression models involves evaluating whether the independent variable (predictor) has a statistically significant effect on the dependent variable (response).
This process typically involves several steps:
1. Formulate the Hypotheses:
Null Hypothesis (H0): The slope of the regression line β1 is zero, indicating no effect of the predictor on the response
Alternative Hypothesis (HA): The slope of the regression line (β1) is not zero, indicating a significant effect.
HA: β1 ≠ 0
2. Estimate the Regression Model:
Y = β0 + β1X + ϵ
Obtain estimates for β0 (intercept) and β1 (slope).
3. Calculate the Test Statistic:
where β^1 is the estimated slope and SE(β^1) is the standard error of the slope.
4. Determine the p-value:
Compare the calculated t-statistic to the t-distribution with n−2 degrees of freedom (where n is the number of observations).
Obtain the p-value associated with the t-statistic.
5. Make a Decision:
Compare p-value to Significance Level (α):
If p-value ≤α reject H0; conclude that the predictor is significant.
If p-value >α , fail to reject H0; conclude that there is insufficient evidence to claim the predictor is significant.