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Residuals
Linear Equation
Definitions
Y values
Correlation
100
What is the equation for the residual?
e = y - (y-hat)
100

What is the equation for linear regression?

y-hat = a + b1*x

100

Change in y over change in x is the ___

slope

100

What does the y intercept tell us?

The value of the y variable when x is 0. 

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

What is another word for the independent variable?

Explanatory

200

What is extrapolation?

Using data outside our range.

200

If two variables are negatively correlated, what value of r would show the strongest correlation?

-1

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
Explain how y =mx + b is different in stats

It finds the predicted value

300

What does residual mean?

error

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
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. With 14 people working, what would you expect sales to be?
$9,384.76
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
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
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

___ measures the percent of variability in the response variable that is accounted for by the least-squares regression line.

r squared