These are three homework examples for Week 2.

1. Week 2 Three Extra Homework
Examples (3x9)/W
MA 221
Statistics for Decision Making
Professor Brent Heard
Not to be copied or linked to
without my permission

2. (3x9)/W
• 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.

3. (3x9)/W
• 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….

4. (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…

5. (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 -

6. (3x9)/W
• 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 xaxis.
• I will show you what I mean on the next chart.

7. (3x9)/W
• 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.

8. (3x9)/W
• 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

9. (3x9)/W
• 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

10. (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

11. (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.

12. (3x9)/W
• 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

13. (3x9)/W
• 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

14. (3x9)/W
• 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.

15. (3x9)/W
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Hope you enjoyed this…
More examples next week….
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