Question

Discuss the t test and p value as a means of determining importance of regression parameters.

Answer 1

Let us take the following output as a reference for answering the question:

The P value for each term as shown in the output generally analyses the null hypothesis in order to check whether the coefficient can be equal to zero or not.

A low P value indicates that the null hypothesis can't be accepted. In other words, a predictor that has a lower P value is likely to be a meaningful addition to your model as there is a significant change seen in the observation. In addition to it, it can also be stated that if the P value is smaller than the changes that are seen in the predictor's value are related to changes that are seen in the response variable.

On the other hand, if the P value is large, then the null hypothesis is accepted. It means that if the P value is larger than the changes that are observed in the predictor are generally not associated with the changes that are seen in the response.

Normally a confidence level of 955 is taken and in this regard, the value of α is 0.05.

α = 1 - Confidence Level = 1 - 95% = 1 - 0.95 = 0.05

So, if the P value is more than 0.05, than we accept the null hypothesis that the particular coefficient can be zero and if the P value is less than 0.05, then we reject the null hypothesis.

In the above output, the regression equation will be Y = 0.8 + 0,4 * HH

Here, for the Intercept, according to T test, the t value is 2.088 and the corresponding P value is 0.127. as the P value is more than 0.05, it signifies that it is not statistically significant. On the other hand for the other coefficient, it is statistically significant as the P value is less than 0.05.