Question

D. Based on the residuals, is your regression line a reasonable model for the data? Why or why

Answer 1

Answer:

The regression line having minimum residuals, actual values closest to estimated regression line values : depicts the most reasonable data model.

Step-by-step explanation:

Regression is a statistical tool depicting cause effect relationship between independent variable(s) (X) , dependent variable. (Y)

Population Regression Function is the conditional expectation of Yi, based on given Xi.

E (Yi / Xi ) = $\beta 0 + \beta 1 Xi$ ; where Y's value is based on given X values

Sample Regression Function is estimated relationship between Y & X, based on sample study.

y = b0 + b1x1 ; where y is a estimate of Y, b0 & b1 estimates of $\beta 0 , \beta 1$ .

In estimating through SRF: there are residuals, i.e differences between actual & estimated values. The most reasonable regression model  (regression line) is which minimises the residual values, i.e actual values are closest possible to regression estimated values.

For this matter, classical linear regression model uses 'Ordinary Least Squares' regression, which minimises the residual's squared values.