Residual Plots
Presentation
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Medium
+1
Standards-aligned
Rachael Pearson
Used 32+ times
FREE Resource
7 Slides • 9 Questions
1
Probability & Statistics Honors
Assessing Regression Models
2
Residual
Residual = Actual y - Predicted y
3
Multiple Choice
y−hat=113.6−0.921x models the relationship between x=the height of a student in inches and y=the number of steps to walk the length of a hallway. Calculate the residual for a person who is 63 inches tall and takes 59 steps.
3.423
-3.423
5.436
-5.436
4
Open Ended
y-hat=113.6-0.921x models the relationship between x=the height of a student in inches and y=the number of steps to walk the length of a hallway. Interpret the residual of 3.423 from the previous question.
5
Residual Plots
Plots the residuals on the y-axis and the explanatory variable on the x-axis
6
Bad Residual Plots
7
Multiple Choice
8
Multiple Choice
Would the linear model be appropriate?
YES
NO
9
Multiple Choice
10
Coefficient of Determination (r2)
r2 measures the percent of the variability in the response variable that is accounted for by the LSRL
Interpretation: "---- % of the variability in ----- is accounted for by the LSRL"
Roller coasters with larger heights usually go faster than shorter ones. Here is the LSRL for 9 roller coasters. The equation of the regression line for this relationship is y ̂=28.17+0.2143x where x=height in feet and y=maximum speed in mph.
r2 = .887
88.7% of the variability in roller coaster maximum speed is accounted for by our model, y-hat = 28.17 + 0.2143x where x=height in feet and y=maximum speed in mph.
11
Multiple Choice
Can you predict the battery life of a tablet using the price? Using the data from a sample of 15 tablets, the LSRL y-hat=4.67 + 0.0068x was calculated using x=price in dollars and y= battery life in hours. S=1.21 and r2=0.342. Which is the correct interpretation of the coefficient of determination.
34.2% of the variability in battery life is explained by the LSRL with x=price in dollars.
The actual battery life in hours is typically 1.21 hours away from the battery life predicted by the LSRL
There is a weak positive linear association between price in dollars and battery life.
We predict the battery life of a tablet will increase 0.0068 hours for each increase of $1 in price
12
Standard Deviation of Residuals (s)
s measures the size of the typical residual
Interpretation: "The actual ----- is typically ---- away from the amount predicted by the LSRL"
Roller coasters with larger heights usually go faster than shorter ones. Here is the LSRL for 9 roller coasters. The equation of the regression line for this relationship is y ̂=28.17+0.2143x where x=height in feet and y=maximum speed in mph.
S = 10.5
The actual maximum speed of a roller coaster is typically 10.5 mph away from the maximum speed predicted by the model.
13
Multiple Choice
Can you predict the battery life of a tablet using the price? Using the data from a sample of 15 tablets, the LSRL y-hat=4.67 + 0.0068x was calculated using x=price in dollars and y= battery life in hours. S=1.21 and r2=0.342. Which is the correct interpretation of the standard deviation of residuals.
34.2% of the variability in battery life is explained by the LSRL with x=price in dollars.
The actual battery life in hours is typically 1.21 hours away from the battery life predicted by the LSRL
We predict that a tablet that cost $0 would have a battery life of 4.67 hours.
We predict the battery life of a tablet will increase 0.0068 hours for each increase of $1 in price
14
Open Ended
A LSRL is used to model the relationship between y=hurricane days and x=years since 1950. s=3.2 and r2=0.15. Interpret the standard deviation of residuals.
15
Open Ended
A LSRL is used to model the relationship between y=hurricane days and x=years since 1950. s=3.2 and r2=0.15. Interpret the coefficient of determination (r2)
16
How to determine if a model is appropriate
The residual plot shows no pattern
small standard deviation of residuals
Large coefficient of determination (r2)
Probability & Statistics Honors
Assessing Regression Models
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