Week 2 Three Extra Homework Examples (3x9)/WMA 221 Statistics for Decision Making

Professor Brent HeardNot to be copied or linked to without my permission 3 x 9

WS4DM

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•As noted, this term I will continue post three additional homework examples by 9 PM (Mountain Time) on Wednesday evening in the Statcave.

•(3x9)/W just means “3 by 9 PM on Wednesday.”

•This week, I will do problems similar to number 11, 13 and 14.

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•Number 11 Example▫On number 11 in the homework, they are

just trying to get you to match a regression equation with the proper graph.

▫It’s a lot easier than what you might think….

(3x9)/W• Let’s say the question was “Match the regression

equation y = -1.35x + 30.1 with the appropriate graph• The first thing you need to look at is the slope and y

intercept of the equation. Remember from Algebra that equations in the form y = mx + b are said to be in the slope-intercept form where m is your slope and b is your y-intercept.

• Therefore in our example y = -1.35x + 30.1. -1.35 would be the slope and 30.1 would be the y-intercept…

• That usually rules out a couple of your choices…• Let’s look at what we know so far…

(3x9)/W•A negative slope means the line will be going

“down” from left to right like a backslash “\”•The y-intercept is where the line actually hits

the y axis.•So from the equation, -1.35x + 30.1, we know

the line will be “going down” and it hits the y axis at 30.1 (you will know that it hits at about 30)

• If you use the magnifying glass icon, you can view the graph much better. The icon is at the top right of each graph. It looks like this -

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•A word of caution – Some of the graphs are very similar until you look at the larger version of the graph and PAY CLOSE ATTNTION TO THE x-axis.

•I will show you what I mean on the next chart.

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•Compare choices “A” and “C”At first glance they look similar, but look closely at the x-axis. “A” goes to 40 and “C” goes to 60. You can get a rough estimate of the slope. For estimation, let’s say they hit the y-axis at 50 or at the point (0,50).

Looking at choice “A” the line passes through a point about at (20,30) . In other words when x is 20, y is 30. The slope could be estimated by getting the difference in y’s over the difference in x’s (30-50)/(20-0) which is -20/20 or “about -1.”

Similarly for Choice “C,” using the points (0,50) and (30,35) the slope would be around (35-50)/(30-0) = -0.5 (which is a big difference)

In this problem, the equation had a slope of -1.04, so I would definitely pick Choice “A”

Don’t worry about the “red dots” on this one.

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•Number 13 Example▫On number 13, they just want you to

understand that the coefficient of determination “r2” is literally the linear correlation coefficient “r” squared.

▫Example on the following page

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•Let’s say they give us a linear correlation coefficient of r = 0.045 and ask the following questions▫Calculate the coefficient of determination

Well it’s r2, so I simply find (0.045)2 which is 0.002025

They wanted it rounded to three decimals, so I would input the number 0.002

Continued on the next page

(3x9)/W▫What does this tell you about the explained

variation of the data about the regression line. Well, the number we used was 0.002, to

convert it to a percentage, we move the decimal two places to the left and say “0.2%” of the variation can be explained by the regression line.

▫Continued on the next page

(3x9)/W▫What about the unexplained variation?

Easy again, just subtract your answer on the previous problem from 100% or 100% - 0.2% = 99.9%

Therefore the r2 tells me the explained variation and “1 minus r2“ or “100% minus the r2 in percent form” gives me the unexplained variation.

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•Number 14 Example▫This is simply a “plug and chug” multiple

regression equation problem where they give you the equation, you plug the values in for x1, x2, etc. and see what it gives you. Be careful to round properly.

▫Example follows

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•The equation used to predict college GPA (range 0 – 4.0) is y = 0.19 + 0.49x1 + 0.003x2, where x1 is high school GPA and x2 is college board score (range 200-800). Use the multiple regression Equation to predict college GPA for a high school GPA of 3.3 and a college board score of 500.▫We are just going to “plug and chug.” See

following page

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•y = 0.19 + 0.49x1 + 0.003x2, where x1 is high school GPA and x2 is college board score (range 200-800). Predict for GPA of 3.3 and a college board score of 500.

•Answer▫y = 0.19 + 0.49(3.3) + 0.003(500)▫ = 0.19 + 1.617 + 1.5▫ = 3.307 or “3.3” rounded to the nearest

tenth.

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•Hope you enjoyed this…•More examples next week….•Visit me at www.facebook.com/statcave

for Stats•Or www.facebook.com/cranksmytractor

for my column that runs in newspapers in the Southern US