24 JULY 2016
MATH 311
LAB 2 – SCATTERPLOTS, REGRESSION, GENERATING DATA & NORMALITY TEST
DUE: TUESDAY, 11 APRIL AT 2:00 P.M.
Scatterplots and regression:
Let’s begin with some data. A study of the development of young children recorded the age in months at
which each of 21 children spoke their first word and their performance much later in life on the Gesell
Adaptive Test. The results in the table below and available at the class page:
http://www.cwu.edu/~englund/Data.htm
Child Age (months)
1
2
3
4
5
6
7
8
9
10
11
15
26
10
9
15
20
18
11
8
20
7
Gesell Score
95
71
83
91
102
87
93
100
104
94
113
Child Age (months)
12
13
14
15
16
17
18
19
20
21
9
10
11
11
10
12
42
17
11
10
Gesell Score
96
83
84
102
100
105
57
121
86
100
Question 1: Make a scatterplot of this data. To do so, select
Graph>Scatterplot>Simple.
Remember, we are using the age at which the first word is spoken predicts later performance on the
Gesell Exam. So enter the response variable (you have to determine which is the response variable) in the
Y variable and the explanatory variable in the X variable. Lastly, select OK.
Looking only at the scatterplot and before performing any further statistical analysis, does it seem to you
that the variables have a strong association? Record your impressions in your report. Specify exactly
what kind of association you think these variables have. Use correct statistical language!
Of course, you should include the graph in your report. We will make your impressions more precise
throughout this worksheet.
Question 2: Compute the correlation (r) of the data. To have MINITAB compute the correlation, do the
following: Select
Stat>BasicStatistics>Correlation
from the menu. A dialogue box will then open. Click on the Variables box and then double click on
AGE and SCORE in the window on the left. Then select OK. The “Pearson correlation of
Age and Score” value is r. Record this value of r in your report. How does the value of r
correspond with your impressions in question 1?
MINITAB also reports a p-value – disregard this for now.
Question 3: Now produce a regression plot. To get MINITAB to do this, select
Stat>Regression>FittedLinePlot
from the menu. Since we are trying to predict the youngsters score on the Gesell test later in life from the
age at which they first speak, chose AGE as the explanatory variable and SCORE as the response
variable. Of course you should include this graph in your report.
Question 4: Use the equation given by MINITAB to predict the Gesell score of a kid who spoke her first
words at 30 months by plugging 30 in for AGE and solving for SCORE. Include your answer in your
report.
The rest of this lab is devoted to learning valuable skills which are not to be included in your write-up.
Hence, you may wish to close the current worksheet and open a new (and clean) one.
Generating Data
Minitab lives to generate data – you pick the type of distribution the data should have and Minitab does
all the work. For example: let’s suppose you want to generate 10,000 data points of normally distributed
data with a mean of 6 and a standard deviation of 1.8. To do so, use the following commands:
Calc>Random Data>Normal
Enter 10000 in the Generate _____ rows of data box
Enter C1 in the Store in column(s): box
Enter 6 in the Mean: box
Enter 1.8 in the Standard deviation box
Select OK
Pretty cool, huh? Make a histogram of your data to check it.
Repeat the above with Uniformly distributed data (min of –3, max of 7). Make a histogram of to check.
If you wanted to generate, say, 17 columns of normally distributed data, you would enter C1 – C17 in the
Store in column(s) box.
How Normal Is Normal?
Let’s suppose you’re given data. Of course, like any good junior statistician, you wonder about the shape,
center, and spread of these data. Towards that end, you construct a histogram of the data (how else would
you be able to describe the shape?) and notice that the histogram is symmetric and single-peaked. But, is
it normal…? There are distributions that are bell-shaped, but not normal. We need a test!
How do we test data for normality?
One option would be to compute the mean and standard deviation of the data, determine how much of the
data lies within 1 standard deviation of the mean, 2 standard deviations, 3 standard deviations, etc. and
then compare this to the percentages listed in Table A.
OR
The other option is we let Minitab do the work as follows. Have Minitab generate 10,000 rows of
normally distributed data (you just learned how to do this above!). Then use the following commands:
Graph>Probability Plot
Select Single
In the Graph Variables: window, enter the column in which your data lives (probably C1).
Select OK
See how the red dots are pretty much essentially following the blue lines – that tells you that the data are
normally distributed.
Now repeat the above procedure with 10,000 uniformly (or any other non-normally) distributed data (just
pick something besides Normal from the Calc>Random Data menu). The red dots won’t follow the
blue lines – that’s how you know that the data are not normally distributed.
Red dots on line = normal … red dots not on line = not normal. … red dots kinda on the line = kinda
normal. Note, the dots rarely lie on the line at the extreme ends – check this.
Also notice the box to the right of the graph. Of particular interest is the P-Value score.