Residuals
What is the equation for the residual?
r = y - (y-hat)
or
r = actual y - predicted y
What is the equation for linear regression?
y-hat = mx + b
In math, this is the symbol for the slope.
What is m?
In statistics, this is the symbol for the y-intercept.
What is b?
Describe a correlation of -0.9 in terms of strength and direction.
Strong, negative.
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
Two variables produce a negative correlation. How will this affect the slope?
The slope will be negative.
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
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)
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
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
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.
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.
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.
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. The residual when 3 people are working is -176. What is the actual sales when 3 people are working?
$8204.02
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.
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.
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.