Linear Models (Equations)
Residuals / Residual Plots
Misc. Review
s, r^2, and Unusual Features
100
Given the scatter plot and the equation, what does the y-intercept mean in this context?
When the student spends 0 hours on their phone, the amount of battery life remaining for their phone is 9 hours.
100
How do you determine the value of a residual?
actual value - estimated value = residual
100
Given the equation y = 2x + 4, find the predicted value for the point (5,6)
y= 14
100
What 3 concepts should you discuss to justify why a point is influential?
Slope
y-intercept
Correlation Value (r)
200
Given the scatter plot and the linear equation, what does the slope mean in this context?
As the time spent on the phone increases by 1 hour, the amount of battery life decrease by .75 hours (3/4 of an hour).
200
True or False: All residuals should be positive.
False. There should a nearly even split of positive and negative residuals for a good line of best fit.
200
Given the equation y = 5.3 + 8.2x , find the predicted value when the x value is 5
y = 46.3
200
Interpret for an s value of 0.3 meters.
The x variable is arm span and the y variable is height. Both measured in meters
The actual height is typically about 2.3 meters away from the height predicted by the model.
300
Given the scatter plot and the linear equation, what does the slope mean in this context?
Equation: y=1+.75x
As the age of the person increases by 1 year, the amount of hours reading increases by .75 hours (3/4 of an hour).
300
An actual value is given in a scatter plot as (5, -11.5). An equation for a linear model is y=-3x + 2.5. What is the residual for this point?
1
300
What TWO things does the correlation coefficient tell you about a relationship?
Strength and Direction
300
Interpret for an r squared value of .825
The x variable is arm span and the y variable is height. Both measured in meters
About 82.5% of the variability in the height is accounted for by the model.
400
Given the scatter plot and the linear equation, what does the y-intercept mean in this context?
Equation: y=1+.75x
When the age of the person is 0 years old, the amount of time spent reading is 1 hour.
400
The actual value of a point is (1,2), the equation is y=2x+1/2
Is the residual positive or negative?
Negative
400
What 5 things should you discuss when asked to "Describe a distribution"
Context
Strength
Direction
Form
Unusual Features
400
How do you justify WHY a point is an outlier?
Discuss that the point has a high residual as compared to the other points in the distribution.
500
Does the y-intercept make sense in this context?
Equation: y=1+.75x
No, if you are 0 years old, it does not make sense to be reading 1 hour.
500
A residual plot shows what about a linear model?
Whether a linear model is appropriate and the accuracy of the actual value to the estimated value. Smaller residuals indicate more accuracy
500
Order the correlation values from strongest to weakest
0.8
-0.25
0.28
-1
0.7
-0.5
0.12
-1
0.8
0.7
-0.5
0.28
-0.25
0.12
500
How do you justify WHY a point is a high leverage point?
Discuss that the point has a high or low x-value as compared to the other x-values in the distribution.