Warm-upO Turn in HW – Ch 8 WorksheetO Complete the warm-up that you picked

up by the door. (you have 10 minutes)

ObjectiveO Define and create Residual Plots. (By

hand and in the calculator.O Use Residual Plots to determine if

using a linear model is appropriate.O Define and calculate R2(Coefficient of

Determination).O Use R2 to explain how much of the

variation is accounted for by the model.

ResidualsO The difference between an observed

value of response variable and value predicted by the regression line..

O e represents residualO represents the predicted response

valueO y represents the actual response

value

ˆresidual y y

y

Residualso Negative residual

means the model OVER PREDICTS the y value.

o Positive residual means the model UNDER PREDICTS the y value.

Residual PlotsO A scatterplot of the residuals against

the explanatory variable.O Help us assess how well a regression

line fits the data.O Should show no obvious pattern.O Should be relatively small in size

Residual Plot PracticeO Do the first page of the Worksheet

Residual Plot (calculator)

O Enter x values in L1 and y values in L2.

O Scroll to put cursor on L3 . Press 2nd ,STAT, Enter, 1. (RESID) This calculates the residuals and puts them in L3 .

O Go to STAT PLOT. Turn on Scatterplot. Pick L1 for X list, and L3 (RESID) for Y list. ZOOM 9

Residual Plot PracticeO Go back to your worksheet. Do # 4

using your calculator to create the scatterplot.

Standard Deviation of Residuals

O Give the approximate size of a “typical” or “average” prediction error.

O This can be found on the calculator by using STAT-CALC-1-Var Stats for the Residuals and looking up standard deviation.

Coefficient of Determination

O R2 is the fraction of the variation in the values of y that is accounted for by the LSRL of y on x.

Interpreting R2

O “ __(R2)_% of the variation in _(response variable)_ is accounted for by the linear model relating _(response variable) to _(Explanatory variable) .

O Example: From the Roller Coaster warm-up, where

O If we calculate that R2 is .82 we would interpret that by saying “82% of the variation in duration of the ride is accounted for by the linear model relating duration to initial drop.”

Is the linear model appropriate?

O Scatter plot must meet the “Straight enough condition”

O Correlation Coefficient- O Residual Plot – random & not too far

from the line.