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

Two variables produce a negative correlation. How will this affect the slope?

The slope will be negative.

200

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

200

R2 has a value of .81 for the relationship between two variables.  What is the value of r?

Can not be determined (either +.9 or -.9)

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 + 0.6943*Math 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

What is one point that all linear regression equations should go through?

(meanx, meany)   ....Look at the equation to calculate the y-intercept!

300

A restaurant's menu items are compared in terms of correlation. Sugar versus Calories has 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. What is yhe meaning of the y-intercept? (And does it make sense?)

A disk with 0 capacity would be expected to cost $18.61.  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 + 91.34*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.

500

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 is the meaning of the y-intercept and does it make sense?

If no salespeople are working, we'd expect to make $8,106 in sales.  No, when no one is working, there should be no sales. This is just a starting point for the data.

500

The r2 value for GDP and "crowdedness" (number of people per room in homes) has a value of 0.46. What does this mean?

46% of variation in crowdedness can be explained by the relationship with GDP.

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