warm-up o turn in hw – ch 8 worksheet o complete the warm-up that you picked up by the door. (you...
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![Page 1: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/1.jpg)
Warm-upO Turn in HW – Ch 8 WorksheetO Complete the warm-up that you picked
up by the door. (you have 10 minutes)
![Page 2: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/2.jpg)
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.
![Page 3: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/3.jpg)
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![Page 5: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/5.jpg)
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ResidualsO The difference between an observed
value of response variable and value predicted by the regression line..
![Page 9: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/9.jpg)
O e represents residualO represents the predicted response
valueO y represents the actual response
value
ˆresidual y y
y
![Page 10: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/10.jpg)
Residualso Negative residual
means the model OVER PREDICTS the y value.
o Positive residual means the model UNDER PREDICTS the y value.
![Page 11: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/11.jpg)
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
![Page 12: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/12.jpg)
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Residual Plot PracticeO Do the first page of the Worksheet
![Page 14: 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)](https://reader035.vdocuments.us/reader035/viewer/2022070413/5697bff11a28abf838cbb6da/html5/thumbnails/14.jpg)
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
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Residual Plot PracticeO Go back to your worksheet. Do # 4
using your calculator to create the scatterplot.
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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.
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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.
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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.”
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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.