Example:
Test the significance of the coefficient of the variable “fraction of the two wheelers” used in the regression model discussed in the previous lecture.
The model is y = -2.2044x + 2.4655
Take the significance level as 5%.
Hypotheses are formulated as follows;
Null hypothesis: m=0
Alternate hypothesis: m≥0
If it is assumed that the error term is normally distributed since the sample size used for the regression is small the statistics follow t-distribution. The critical t-value corresponding to 5 % significance with 10 degrees of freedom is: 1.812

To get the standard error of the statistic we need;

Since the t_cal is less than the critical t-value corresponding to 5 % significance the conclusion of the testing is “failed to reject the null hypothesis”. In other words, the coefficient is not significantly different from zero and the independent variable is not significant in explaining the variability of the dependent variable.