AP STATS
Linear Regression Chapter 8
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Linear Regression
Objective:
The following is a scatterplot of total fat versus protein for 30 items on the Burger King menu:
What is linear regression?
Regression and Residuals
AP STATS
Linear Regression Chapter 8
Negative Residual
Positive Residual
Line of Best Fit
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AP STATS
Linear Regression Chapter 8
Name _______________________________
Date _______________ Period 1 2 3 4 5 6 7
Slope of the Regression line
Y-intercept of the Regression line
Residuals Revisited
Example:
Given the regression line for the previous scatter plot
Ŷ = 6.413 + 0.9769x
Predicted Fat = 6.413 + 0.9769protein
What is the meaning of slope?
What is the meaning of the y-intercept?
How much fat would we expect an item with 12 grams of protein to have?
How much protein would an item with 15 grams of fat have?
A Double Whopper sandwich has 48 grams of Protein and 58 grams of fat. What is the residual
in fat for this sandwich?
AP STATS
Linear Regression Chapter 8
Name _______________________________
Date _______________ Period 1 2 3 4 5 6 7
Example: Select sandwiches from Burger King
Item
Whopper
Whopper with cheese
Big King
Hamburger
Cheeseburger
Tendergrill chicken
Original Chicken
Big Fish Sandwich
BK Veggie Burger
Grams of Fat
37
44
31
9
12
21
40
28
16
Calories
650
730
530
230
270
460
660
520
390
What is the regression line for the data?
What is the slope in the context of the problem?
What is the y-intercept in the context of the problem?
A sandwich with 15 grams of fat would be expected to have how many calories?
A sandwich with 450 calories would be expected to have how many grams of fat?
A Bacon Cheeseburger has 13 grams of fat and 290 total calories, what is the residual in calories
for this sandwich?
AP STATS
Linear Regression Chapter 8
Conditions required for the model to be a good fit
R-Squared
Residual Plot
What not to do
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AP STATS
Linear Regression Chapter 8
Name _______________________________
Date _______________ Period 1 2 3 4 5 6 7
Example : Breakfast Cereal
The following is data from 77 different breakfast cereals comparing the relationship of sugar in
the cereal and the amount of calories with each cereal.
R = 0.564
Calories mean – 107.0 SD – 19.5
Sugar mean – 7.0 grams, SD – 4.4
What is the slope of regression line?
What is the y – intercept?
Write the regression equation?
Interpret the model
Example: Urban Planning
We want to estimate the costs per person associated with traffic delays
2002 Urban mobility report (70 cities in 2000)
Annual cost person
mean - $298.96 SD - $180.83
Average speed per person
mean – 54.34 mph, SD 4.494 mph
R = -0.90
Write an equation to model this situation
What does the slope mean?
What is the y – intercept and what does it mean?
Interpret the model
AP STATS
Linear Regression Chapter 8
Name _______________________________
Date _______________ Period 1 2 3 4 5 6 7
What to watch out for in Linear Regression
1. Extrapolation
2. Influential Points
3. Lurking Variable
4. Straight lines that are not straight
5. What to do
a. Examine the residual plot
b. Examine the R-squared
Example: Data collected from the study of water pollution caused by commercial and domestic
waste.
Day (x)
1
2
3
5
7
10
Oxygen Demand (y)
109
149
149
191
213
224
Square root (y)
Log (x)
Log (y)
AP STATS
Linear Regression Chapter 8
Name _______________________________
Date _______________ Period 1 2 3 4 5 6 7