Residuals
How do you find the residual of a data point?
Residual = Actual - Predicted
Predicted Price = 18.617 + 103.929 Capacity.
This is the regression equation for disk space Capacity (in megabytes) versus Price (in dollars) at a local store. What does the slope of 103.929 mean in this context?
For every 1 mb increase in capacity, the price increases by $103.929.
List the steps to find the linear regression of a line given a data set in your calculator.
1) Hit Stat, Edit, Enter data in Lists 1 and 2
2) Hit Stat again, then CALC Linear Regression (4)
In slope intercept form, this variable represents the y-intercept.
What is b?
Describe a correlation of -0.9 in terms of strength (weak, moderate, or strong) and direction.
Strong, negative.
With an observed value of 25.8 and a predicted value of 45.9, what is the residual?
-20.1
Predicted Price = 18.617 + 103.929 Capacity.
This is the regression equation for disk space Capacity (in megabytes) versus Price at a local store. With a capacity of 2 mb, what would you expect the price to be?
$226.475
What variable is used to represent the correlation coefficient?
r
What does r = -0.75 tell us about a linear regression?
It has a fairly strong, negative correlation
Ms. Tey will check your boards
What does a negative residual indicate - where is the observed value in comparison to the predicted value?
The observed is below the predicted value.
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34 Number of Sales People Working. What does the slope mean in this situation?
For every increase of 1 sales person working, sales increase by $91.34.
You have your lists populated with a data set. What do you do to find predicted values for your linear regression of your data set?
In List 3, you enter in your linear regression equation, but instead of x, type in L1 (your inputs), then hit enter
The linear model for a local store's Number of Sales people working versus Sales is as follows:
Sales = 8,106 + 91.34 (# Sales People Working)
What is the y-intercept?
$8,106
A restaurant's menu items are compared in terms of correlation. Sugar versus Calories have a correlation of 0.25. Sugar versus Protein has a correlation of -0.68. Which has a stronger correlation?
Sugar versus Protein.
The linear model for a local store's Number of Sales people working versus Sales is as follows:
Sales = 8,106 + 91.34(# of Sales People Working)
With 14 people working, what would you expect sales to be?
$9,384.76
How do you use your calculator to find the residuals of a data set?
Then, in a list, go to 2nd Stat (LIST) and hit RESID
How do you find the reasonable range for a predicted value?
A student says, "There was a very strong correlation of 1.22 between Sugar and Fat content." Explain the mistake made here.
Correlation is between -1 and +1.
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34 (Number of Sales People Working). If two people are working, the observed value is $8600. What is the residual?
$311.32
An analysis of Math SAT versus Verbal SAT scores gives an equation of -
Predicted Verbal SAT Score = 171.333 + 0.6943Math SAT Score.
What would you predict someone's verbal score to be if they got a 520 on their Math section?
532.369
What should you ALWAYS bring to Ms. Tey and Ms. Cooper's class?
YOUR CALCULATOR!!!
The linear model for a local store's Number of Sales people working versus Sales is as follows:
Sales = 8,106 + 91.34 (# of Sales People Working)
Does the y-intercept have meaning in this equation?
No, when no one is working, there should be no sales. This is just a starting point for the data.
Two variables produce a negative correlation. How will this affect the slope?
The slope will be negative.