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Hypothesis Testing of Coefficients

  • The values of the slope coefficients doesn't tell anything about their significance in explaining the dependent variable
  • Even an unrelated variable when regressed would give some value of slope coefficients
  • To exclude the cases where the independent variables doesn't significantly explain the dependent variable, we need the hypothesis testing of the coefficients for checking whether they contribute in explaining the dependent variable significantly or not
  • The t-statistic is used to check the significance of the coefficients
  • The t-statistic used for the hypothesis testing is same as used in the hypothesis testing of coefficient of simple linear regression
  • Following are the hypothesis and alternative hypothesis to check the statistical significance of bk:
  • Hypothesis H0: bk =0
  • Alternative Hypothesis (Ha): bk ≠ 0
  • The t-statistic of (n-k-1) degrees of freedom for the hypothesis testing of the coefficient bk


If the value of t-statistic lies within the confidence interval, H0 can't be rejected.


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