## Hypothesis testing in Simple regression models

Simple regression models are used to study the relationship between a single independent variable (also known as the predictor variable) and a single dependent variable (also known as the response variable). Hypothesis testing is an important tool in simple regression analysis for testing the significance of the relationship between the two variables. The following are the steps involved in hypothesis testing in simple regression models:

- Define the null and alternative hypotheses: The null hypothesis states that there is no significant linear relationship between the independent variable and the dependent variable, while the alternative hypothesis states that there is a significant linear relationship between the two variables.
- Determine the level of significance: The level of significance (also known as alpha) is the probability of rejecting the null hypothesis when it is actually true. A common level of significance is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.
- Collect the data: Data is collected for the independent and dependent variables for each observation in the sample.
- Calculate the regression equation: The regression equation estimates the relationship between the independent variable and the dependent variable. It is calculated using the method of least squares.
- Calculate the test statistic: The test statistic is used to determine the p-value, which is the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming that the null hypothesis is true. The test statistic is calculated as the ratio of the estimated slope coefficient to its standard error.
- Determine the critical value: The critical value is the value that separates the rejection region from the non-rejection region. The critical value is determined based on the level of significance and the degrees of freedom.
- Compare the p-value to the level of significance: If the p-value is less than the level of significance, then the null hypothesis is rejected and the alternative hypothesis is accepted. This means that there is a significant linear relationship between the independent variable and the dependent variable. If the p-value is greater than the level of significance, then the null hypothesis is not rejected, and it is concluded that there is no significant linear relationship between the independent variable and the dependent variable.

Hypothesis testing is an important tool for understanding the significance of the relationship between the independent variable and the dependent variable in a simple regression model. It allows us to draw conclusions about the relationship between the two variables based on the sample data.

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