Show:
Residuals
Linear Equation
Slope
Y-intercept
Correlation
100
What is the equation for the residual?
e = y - (y-hat)
100
What is the equation for linear regression?
y-hat = b0 + b1*x
100
In statistics, this is the symbol for the slope.
What is b1?
100
In statistics, this is the symbol for the y-intercept.
What is b0?
100
Describe a correlation of -0.9 in terms of strength (weak, moderate, or strong) and direction.
Strong, negative.
200
With an observed value of 25.8 and a predicted value of 45.9, what is the residual?
-20.1
200
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
200
This is the equation for the slope in statistics.
What is Average Y - b1*Average X?
200
This is the equation for the y-intercept in statistics.
What is r*(Sy/Sx)
200
Which linear regression equation is correlation used in?
Slope.
300
What does a negative residual indicate - where is the observed value in comparison to the predicted value?
The observed is below the predicted value.
300
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?
What is 532.369
300
You are given r = 0.45, Sy = 28 and Sx = 54. What is the slope?
0.2333
300
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34Number of Sales People Working. What is the y-intercept?
$8,106
300
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.
400
Linear model A creates a sum of least squares of 1,500 and B creates a sum of 480. Which model should you use? Why?
Model B - it's lower.
400
How can you tell if a linear equation is accurate?
r-squared and the individual residuals
400
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.
400
Predicted Price = 18.617 + 103.929 Capacity. This is the regression equation for disk space Capacity versus Price at a local store. Does the y-intercept have meaning?
No, no one would buy a disk with zero capacity.
400
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.
500
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34Number of Sales People Working. If two people are working, the observed value is $8600. What is the residual?
$311.32
500
How can you tell if a linear model is reliable?
residual plot!
500
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34Number 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.
500
The linear model for a local store's Number of Sales people working versus Sales is as follows: Sales = 8,106 + 91.34Number 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.
500
Two variables produce a negative correlation. How will this affect the slope?
The slope will be negative.