Simple Linear Regression -

Problem Definition: Midwest Insurance wants to develop a model able to predict sales according to time with the company.

Evaluate the bivariate graph to determine whether a linear relationship exists and the nature of the relationship. What happens to y as x increases?  What type of relationship do you see? 

Simple linear regression assumes that the relationship between the dependent, y and independent variable, x can be approximated by a straight line. 

Least Squares Regression Properties 

1. The sum of the residuals from the least squares regression line is 0. The total under prediction by the regression model is exactly offset by the total over prediction. The probability distribution of ε is normal.  

2. The sum of the squared residuals is a minimum (residuals are error measurements) ∑(y-y')².

3. The simple regression line always passes through the mean of the y variable and the mean of the x variable. 

4. The least squares coefficients b₀ and b₁ are unbiased estimators of their corresponding population parameters β₀ and β₁.

Attachment:- Assignment.rar