Regression Equations and Residuals

• 50 miles

• -50 miles

• 8 miles

• -25 miles

When using midterm exam scores to predict a student's final grade in the class, the student would prefer to have

• positive residual, because that means the student's final grade is higher than we would predict with the model

• positive residual, because that means the student's final grade is lower than we would predict with the model

• residual equal to zero, because that means the student’s final grade is exactly what we would predict with the model

• negative residual, because that means the student’s final grade is higher than we would predict with the model

How do you calculate a residual?

• Observed - Predicted

• Predicted - Observed

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

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• 
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The regression equation y = 25x + 100 models the cost, y, of an event for x people.

The table shows what the party sizes actually paid. Complete the table with the predicted values and residuals.

e

f

g

h

d

c

225

300

-35

15

underestimate

overestimate

35

-15

In the context of bivariate data, what does the term "residual" refer to?

• The difference between the observed value and the predicted value.

• The slope of the regression line.

• The y-intercept of the regression line.

• The correlation coefficient.

What does a residual value of 1.3 mean when referring to the line of best fit of a data set

• a data point is 1.3 units above the line of best fit

• A data point is 1.3 units below the line of best fit

• The line of best fit has a slope of -1.3

• The line of best fit has a slope of 1.3

1) 

• A

• B

• C

• D

A person travels by car.  They record their miles driven in a data table.  Calculate the linear regression equation of this data.

• y = 61.93x - 1.79

• y = -1.79x + 61.93

• y = 0.016x + 0.03

• y = 0.03x + 0.016