Regression Equations and Residuals

Standard deviation of residuals s...

• The standard deviation of the residuals s measures the size of a typical residual.

• That is, s measures the typical distance between the actual y values and the predicted y values.

Which of the following definitions are true...

• Points with high leverage in regression have much larger or much smaller x values than the other points in the data set.

• An outlier in regression is a point that does not follow the pattern of the data and has a large residual.

• An influential point in regression is any point that, if removed, substantially changes the slope, y intercept, correlation, coefficient of determination, or standard deviation of the residuals.

• All of the above

A ______________ regression line makes the residuals as small as possible.

• good

• bad

• ugly

• mean

To determine whether the regression model is appropriate, look at the residual plot.

• 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.

The ___________________ measures the percent of the variability in the response variable that is accounted for by the least-squares regression line.

• coefficient of determination

• coefficient of relaxation

If the line of regression is y = 3.45x - 6.7 and the actual point is (5,12), what is the residual for that point?

• 45

• -1.45

• 34.7

• -34.7

What is a line of best fit used for?

• To make predictions

• To make the graph look pretty

• To connect the points

The linear regression equation is y = 61.93x - 1.79.  According to the model, the slope can be interpreted as:

• After 0 hours of driving, they went 61.93 miles.

• They drove at a speed of 61.93 miles per hour.

• They drove 61.93 miles total.

• They drove 61.93 hours total.

The results of a linear regression are shown.

Which phrase best describes the relationship between x and y?

• strong negative correlation

• strong positive correlation

• weak negative correlation

• weak positive correlation

The linear regression equation is y = 61.93x - 1.79.  Use the equation to predict how far this person will travel after 10 hours of driving.

• 10 miles

• 617.5 miles

• 0.19 miles

• 500 miles