Warm-up
O Turn in HW – Ch 8 Worksheet
O Complete the warm-up that you picked up by the
door. (you have 10 minutes)
Objective
O 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.
Residuals
O The difference between an observed value
of response variable and value predicted by
the regression line..
residual  y  yˆ
O
e represents residual
O 𝑦 represents the predicted response value
O y
represents the actual
response value
ŷ
Residuals
o Negative residual
means the model
OVER PREDICTS the
y value.
o Positive residual
means the model
UNDER PREDICTS
the y value.
Residual Plots
O 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 Practice
O 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 Practice
O 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.
O𝑠 =
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙𝑠 2
𝑛−2
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 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = 91.033 + 0.242(𝑑𝑟𝑜𝑝)
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- 𝑟 𝑐𝑙𝑜𝑠𝑒 𝑡𝑜 1.
O Residual Plot – random & not too far from
the line.