A Regression Example where we draw the fitted line though the data.
The data presented in this example are of Age and Price of used Saturn
automobiles.
Enter the data:
In c1 enter Age (x) 6, 5, 4, 3, 2, 2, 1, 1.
In c2 enter Price (y) 6, 9, 8, 10, 11, 12, 11, 13.
When performing linear regression analysis the first step is to plot the
data in a scatterplot. To create a scatterplot click Graph, then
Plot, for Y click on Price and for X click on Age,
and finally click OK. The commands should look like this:
MTB > Plot 'Price'*'Age';
SUBC> Symbol;
SUBC> ScFrame;
SUBC> ScAnnotation.
Next we will calculate the descriptive statistics of the x and y
data. First, click Stat, then Basic Statistics, then Display
Descriptive Statistics, then click both Age and Price, and
finally OK. The output should look as follows:
MTB > Describe 'Age' 'Price'.
Descriptive Statistics
Variable N Mean Median TrMean StDev SE Mean
Age 8 3.000 2.500 3.000 1.852 0.655
Price 8 10.000 10.500 10.000 2.268 0.802
Variable Minimum Maximum Q1 Q3
Age 1.000 6.000 1.250 4.750
Price 6.000 13.000 8.250 11.750
Next we calculate the correlation coefficient. First click Stat,
then Basic Statistics, then Correlation, then click both Age
and Price, and finally OK. The output should look as follows:
MTB > Correlation 'Age' 'Price'.
Correlations (Pearson)
Correlation of Age and Price = -0.919, P-Value = 0.001
Note that the correlation coefficient is negative indicating a negative
relationship!
Next we will calculate the regression line and save the fitted values from
the regression line so we can draw the regression line on a scatterplot with
the data. To calculate the regression line click Stat, then click
Regression, then Regression, enter Price for the Response
and Age for the Predictor. The output should be as follows:
MTB > Regress 'Price' 1 'Age';
SUBC> Constant;
SUBC> Brief 2.
Regression Analysis
The regression equation is
Price = 13.4 - 1.12 Age
Predictor Coef StDev T P
Constant 13.3750 0.6847 19.54 0.000
Age -1.1250 0.1976 -5.69 0.001
S = 0.9682 R-Sq = 84.4% R-Sq(adj) = 81.8%
Analysis of Variance
Source DF SS MS F P
Regression 1 30.375 30.375 32.40 0.001
Residual Error 6 5.625 0.938
Total 7 36.000
The last thing we will do is plot the data along with the fitted line on
the same scatterplot. To do this click Stat, then Fitted Line Plot,
then enter Price for Y and Age for X. Next click
the OK button.
Simulate rolling a fair die
Minitab allows you to generate what are called ``random numbers.'' As an
example of how to do this we will simulate rolling a fair die. Minitab has a
command that simulates equally likely integer values in a range defined by the
user. To do this click Calc, then Random Data, then click on
Integer.
We will run 3 simulations of increasing size. To start we will simulate 10
rolls of a fair die. Enter the number 10 in the Generate box,
next enter c1 in the Store in column(s) box, then enter 1
in the Minimum value: box and 6 in the Maximum value box,
then click OK. You should get 10 numbers in the first column.
Next we will make a histogram of our random data. Click Graph, then
Plot, then Histogram, then enter c1, and OK. Does
the histogram appear as we would expect? Recall that each side of a die has a
1/6 probability of occurring.
Redo the simulation with the number of 100 in the Generate
box. Redo the histogram. What do you see now? Redo it again with 200.
What do you see in the histogram?
How to take a random sample from a list.
We will now use Minitab to take a Simple Random Sample from a list of
names. Minitab has a command that will randomly select a sample of a specific
size n from a list given in a column.
To do this we will take a sample of size n = 4 from a list of 10 names.
First, enter 10 names down the fist column c1:
Ed, John, Kim, Fred, Ted, Tom, Jim, Julie, Wes, Robert
To select a random sample from this list of 10 people, click Calc,
then Random Data, the Sample From Columns. Enter 4 in the
Sample box, then enter c1 in the rows from column: box,
then enter c2 in the Store samples in: box, and finally OK.
This produces a random sample in Minitab.