3.1 Interpreting fitted models
Fitted models
A population linear regression line has the form , where is the intercept parameter and is the slope parameter. Since and are rarely known, estimators and are needed to build linear models used for predicting the value of the response variable . The sample linear regression line is , which gives the fitted values for .

The animation below gives the reaction times (in milliseconds) of adult drivers after consuming alcohol (in standard drink units). Reaction time is the response variable and alcohol consumption is the explanatory variable.

PARTICIPATION ACTIVITY
3.1.1: Estimates for the slope and intercept regression parameters.


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Alcohol consumption,




Reaction time,




























The represents the slope of the line, which is .

Captions
The sample simple linear regression line represents the linear relationship between and .
represents the -intercept of the line, or the fitted value of when .
The fitted value of increases from to and increases from to . The slope is the change in , denoted by divided by the change in , denoted by .
The represents the slope of the line, which is .

Feedback?
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3.1.2: Estimates for the slope and intercept regression parameters.
Refer to the animation above.

1)
What is the estimate for the intercept parameter?
Correct

The -intercept is the fitted value of when is , which is .
2)
What is the estimate for the slope parameter?
Correct

Two points on the regression line are and . Computing the slope gives the ratio , which is the estimate of the slope parameter.