Answer
The simple regression.
The regression equation can be defined as follows:
\[{{\hat{y}}_{t}}={{\beta }_{1}}{{x}_{t}}+{{\beta }_{0}}+{{\varepsilon }_{t}}\]
Here,\[{{\hat{y}}_{t}}\]is the predicted value of the dependent variable and \[{{x}_{t}}\]is the value of the independent variable. The slope of the regression line is \[{{\beta }_{1}}\] and the intercept of the regression line is \[{{\beta }_{0}}\]
The error term is represented as \[{{\varepsilon }_{t}}\]
The requirements of the least-square regression are
1. The mean of the response value is linearly dependent on the independent variable.
2. The dependent variable has a normal distribution whose mean and standard deviation are\[{{\mu }_{y|x}}={{\beta }_{1}}x+{{\beta }_{0}}\]and \[\sigma \]
respectively.
To check whether the requirements are fulfilled by the data or not, the residuals are plotted and it is checked whether the distribution of the residuals is standard normal. The residual plot and the normal probability plot are used to check the requirements.
Work Step by Step
Given above.
