1. Yesterday, using Worksheet 8, we did a simple problem by hand, and you should have discovered the following relation:
SSE =
2
( )
xy
yy
xx
SS
SS SS
. The appropriate numbers in this equation were
2
11.4
1.808 26.8 5.2
which reduces to
1.808 = 26.8- 24.992. Get into Minitab and enter the data from Worksheet 8. Then do the regression to predict quiz score from
study time. Identify where all of these quantities appear and what they are called. From yesterday’s class, you discovered that the
person using Scheme I with
y
as their regression predictor has a sum of squares of prediction errors = to 26.8. The person using
Scheme II with x as a predictor, has SSE=1.808, which is quite a bit smaller than 26.8. How much smaller? 24.992 smaller. We
could say that the regression user does better by the amount 24.992. This is called the Sum of Squares due to Regression. Now,
using your Minitab results, note that R2 = 93.8% (or .938 as a decimal). Using only the numbers from the above relation,
determine how to calculate R2. This is exceedingly important. Can you formulate a way of describing how much better a
regression user does than a non-regression user?
2. In class you took the (x,y) data from Worksheet 7 (The “Eyeballing a line” worksheet with data on Thai restaurant sales) and
used your calculator (if it has regression capabilities) to predict y from x. Now, using Minitab, put the x data in C1 and the y
data in C2. Before doing anything else, plot the data. Go to the Graph menu, select Scatter Plot and continue by filling in the
necessary boxes. After you have done this, type the following command at the Minitab prompt, exactly as it is shown: plot
c2*c1. You can take your pick as to which way to plot is faster. Next, type the following command at the Minitab prompt in
the session window:
regress C2 1 C1.
This instructs Minitab to predict y in C2 from 1 x-variable located in C1. Compare the output with what you got by using your
calculator. Be sure you can locate SSE---it is under the SS column for Residual error. Also, locate SSyy. Now, as an alternative
approach, use the menus to get the regression. Go to Stat, Regression, and then Regression. Put C2 in the response variable box
and C1 in the predictor variable box. Hit OK until you get the output. Be sure you can correctly interpret the values of a and b in
the context of the problem. i.e., be able to put the answers in terms of the student population and sales at the Thai restaurants.
Another alternative approach, which you may find preferable, is to again use the Stat menu, select regression, and then Fitted
Line Plot. Redo the previous work using this approach. Check the output here as well.
After you have done this, be sure you can interpret the values of a and b and r2. Also, determine how to calculate r2 from the
Minitab output. (i.e., if someone covered up the r2 value, could you obtain it easily from the rest of the Minitab output?)
3. Word has it that there is a CWU student from Yakima who commutes daily to Ellensburg. Before she leaves she
has a latte to make sure she stays awake on the trip. As she loves coffee, she sometimes has more than one shot
of espresso.
Here are some data on various days:
X = Number of shots espresso
Y = Time it takes for her commute.
X 0 2 3 1 4 2 1
Y 75 50 45 55 25 48 60
a) Find the best fitting line for predicting her commute time based on the number of shots of espresso. Be sure to
experiment with the various ways of doing this in Minitab (the alternative ways discussed in problem 2).
Math 311 Fall 2008 Minitab Lab 2---Regression Analysis
