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.
r=1/{n-1}\sum{z_xz_y}
Correlation
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
b=r\frac{s_y}{s_x}
Slope
What does r = -0.75 tell us about a linear regression?
It has a fairly strong, negative correlation
Sketch a data set with a correlation correlation of -0.98.
Hold your work up to the screen!
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.
a=\overline{y}-b\overline{x}
y-intercept
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
\hat{y}=a+bx
Least Squares Regression Line
or
Equation for the linear model
What is a data point that has an "extreme" x and y coordinate called?
Influential Point
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
y-\hat{y}
residual
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 downhill (negative).