Fitting Lines Residuals

Residuals are . . . 

• possible models not explored by the researcher

• variation in the response variable that is explained by the model

• the difference between the observed response and the values predicted by the model

• data collected from individuals that is not consistent with the rest of the group

After performing analyses on a set of data, Mrs. Schoeneck examined the scatter plot of the residual values for each analysis. Which scatter plot indicated the best linear fit for the data?

• A

• B

• C

Shown is a residual plot. Would a linear regression model of the data be most appropriate?

• YES

• NO

Shown is a residual plot. How many positive residuals are there?

• 5

• 1

• 3

• 9

• y = 1.45x + 22
• y = -2x + 15
• y = 1.33x + 30
• y = -1.5x + 24

Shown is a residual plot. How many negative residuals are there?

• 5

• 1

• 3

• 9

What is the line of best fit for the data?

• y = .25x + 8.25

• y = 8.25x + .25

• y = x + 1

What is the equation of the line of best fit?

• y= 6x + 2

• y = -2x +6

• This residual plot represents a linear fit.
• This residual plot represents a nonlinear fit.
• This residual plot represents no fit.

The residual plots from five different least squares regression lines are shown below. Which of the plots shows the strongest evidence that its regression line is an appropriate model for the data and is consistent with the assumptions required for inference for regression?

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