Least Square Regression Models and Residuals

y=mx+b

y=a+bx

$$y^{\wedge}=a+bx$$

When asked to interpret the slope or y intercept, it is very important to include the word predicted (or equivalent) in your response.

a is the y-intercept

using the regression line to make a prediction for x=0 is an extrapolation

b is the slope, the amount by which the predicted value of y

changes when x increases by 1 unit

good

bad

linear

non-linear

If there is no leftover curved pattern in the residual plot, the regression model is appropriate.

If there is leftover curved pattern in the residual plot, the regression model is appropriate.

If there is a leftover curved pattern in the residual plot, consider using a regression model with a different form.

If there is not a leftover curved pattern in the residual plot, consider using a regression model with a different form.

coefficient of determination

$$x^2$$  

$$r^2$$  

coefficient of relaxation

.921

.925

.961

-.961

4.292

The predicted income will increase by $31.45 for each hour worked

The hours worked will increase by $31.45 for each additional dollar income

The predicted income will decrease by $242.3 for each hour worked

The hours worked will increase by $242.3 for each additional dollar income