Non-Linear Relationships

Residual Plots

When discussing an association, we look at

the following elements: D O F S

Correlation can help us identify the ________ and ________ of the linear association.

Try this …

irectionutlier

ormtrength

directionstrength

_______ are easily spotted.

Correlation does not indicate what the _____ of the association is.

A ___________ can help us make a decision as to which model would produce the best prediction.

Form

Outliers

form

residual plot

Which is a Residual Plot?

Making a Residual Plot

Shoe Size

Height (actual)

Height (predicted)

Residual

12.6 74

11.8 65

12.2 71

11.6 67

12.2 69

11.4 68

12.8 70

12.2 69

11.8 71

12.6 72

ŷ = 25.3 + 3.66x

72.14867.024

67.756

69.952

68.48871.416

2.584-3.4881.048-0.756-0.9520.976-2.148-0.952

Resi

dual

Shoe Size

0

1

2

-2

-1

11

.62.51268.488

69.952

69.95271.416

0.58411

.8 12

.0 12

.2 12

.4 12

.611

.4

-3

3

Your graphing calculator can create the residual plot for you!

Calculator

1. Enter the explanatory variable into L1 and the response variable into L2.

2. Tell the calculator to use the explanatory variable and the residuals.

3. Look at the Residual Plot

If the residual plot is random, you

have found a good model.

If the residual plot takes on a form, the hunt for a good model must continue.

Today’s model ____ good.

Good Choices

Hence, using a linear regression to model today’s association is ___________.

was

appropriate

A least-squares regression line was used to model the relationship between putting average and scoring average for golfers on the 2009 PGA tour. The corresponding residual plot is shown.

Example

Based on the residual plot, is a linear model appropriate for this association?

The point highlighted is for the golfer David Duval. Estimate his residual from the graph and interpret its value.

If you were to predict the scoring average for a golfer with a putting average of 1.86, would you expect your prediction to be too low, too high, or just about right? Explain.

Yes

1.7; In 2009, Duval’s scoring average was about 1.7 strokes more than expected.

Just about right; Residual plot is random it’s a good model.

A residual plot displays the values of the

__________ variable on the horizontal axis and the value of the _______ on the vertical axis.

We use residual plots to determine whether the form of a model matches the form of an __________ between two numerical variables.

The residual plot is appropriate if the plots are ________.

Sum it Up

explanatory

residual

association

scattered

take on a form

The residual plot is inappropriate if the plots _____________.