Note: “A sample session” is adapted from the
Getting Started with Stata for Windows manual.
A sample session
The dataset we will use for this session is about vintage 1978 automobiles
sold in the United States.
To follow along using point-and-click, note that the menu items are given by
Menu > Menu Item > Submenu Item > etc. To follow along using the
Command window, type the commands that follow a dot (.) in the boxed
listing into the small window labeled Command. When the structure of
a command is notable, it will be pointed out as a Syntax note.
Start by loading the auto dataset, which is included with Stata. To
use the menus,
- Select File > Example Datasets....
- Click on Example datasets installed with Stata.
- Click on use on auto.dta.
The result of this command is threefold:
You could have opened the dataset by typing sysuse auto followed by
Enter into the Command window. Try this now. sysuse is a
command that loads (uses) example (system) datasets. As you will see during
this session, Stata commands are often simple enough that it is faster to use
them directly. This will be especially true once you become familiar with the
commands you use the most in your daily use of Stata.
Syntax note: in the above example sysuse is the Stata command, whereas
auto is the name of a Stata data file.
Simple data management
We can get a quick glimpse at the data in the Data Browser. Click on
the Data Editor (Browse) button,
 ; select
Data > Data Editor (Browse) from the menus; or type the command
browse.
When the Data Browser window opens, you can see that Stata regards the data
as one rectangular table. This is true for all Stata datasets. The columns
represent variables, whereas the rows represent observations.
The variables have somewhat descriptive names, whereas the observations are
numbered.
The data are displayed in multiple colors—at first glance it appears
that the variables listed in black are numeric, whereas those that are in
colors are text. This is worth investigating. Click on a cell under the
make variable: the input box at the top displays the make of the car.
Scroll to the right until you see the foreign variable. Click on one
of its cells. Although the cell may display “Domestic”, the input
box displays a 0. This shows that Stata can store categorical data as numbers
but display human-readable text. This is done by what Stata calls value
labels. Finally, under the rep78 variable, which looks to be numeric,
there are some cells containing just a period (.). As we will see,
these correspond to missing values.
Syntax note: here the command is browse, and there are no other
arguments.
Looking at the data in this fashion, though comfortable, lends little
information about the dataset. It would be useful for us to get more details
about what the data are and how the data are stored. Close the Data Browser
by clicking its close button—while it is open, we cannot give any
commands in Stata.
We can see the structure of the dataset by describing its contents.
This can be done either by going to Data > Describe data > Describe data
in memory in the menus and clicking OK or by typing describe
in the Command window and pressing Enter. Regardless of which method
you choose, you will get the same result:
. describe
Contains data from C:\Stata11\ado\base\a\auto.dta
obs: 74 1978 Automobile Data
vars: 12 13 Apr 2009 17:45
size: 3,478 (99.9% of memory free) (_dta has notes)
|
storage display value
variable name type format label variable label
|
make str18 %-18s Make and Model
price int %8.0gc Price
mpg int %8.0g Mileage (mpg)
rep78 int %8.0g Repair Record 1978
headroom float %6.1f Headroom (in.)
trunk int %8.0g Trunk space (cu. ft.)
weight int %8.0gc Weight (lbs.)
length int %8.0g Length (in.)
turn int %8.0g Turn Circle (ft.)
displacement int %8.0g Displacement (cu. in.)
gear_ratio float %6.2f Gear Ratio
foreign byte %8.0g origin Car type
|
Sorted by: foreign
|
If your listing stops short and you see a blue --more-- at the base of
the Results window, press the space bar or click on the blue
--more-- itself to allow the command to be completed.
At the top of the listing, some information is given about the dataset, such
as where it is stored on disk, how much memory it occupies, and when the data
were last saved. The bold 1978 Automobile Data is the short
description that appeared when the dataset was opened and is referred to as a
data label by Stata. The phrase _dta has notes informs us that
there are notes attached to the dataset. We can see what notes there are by
typing notes in the Command window:
. notes
_dta:
1. from Consumer Reports with permission
Here we see a short note about the source of the data.
Looking back at the listing from describe, we can see that Stata keeps
track of more than just the raw data. Each variable has the following:
- A variable name, which is what you call the variable when
communicating with Stata.
- A storage type, which is the way in which Stata stores its data.
For our purposes, it is enough to know that types beginning with str
are string or text variables, whereas all others are numeric. See [U]
12 Data.
- A display format, which controls how Stata displays the data in
tables. See [U] 12.5 Formats: controlling how data are displayed.
- A value label (possibly). This is the mechanism that allows Stata
to store numerical data while displaying text. See chapter 9 and [U]
12.6.3 Value labels.
- A variable label, which is what you call the variable when
communicating with other people. Stata uses the variable label when making
tables, as we will see.
A dataset is far more than the data it contains. It is also the
information that makes the data usable by someone other than the original
creator.
Although describing the data says something about the structure of the data,
it says little about the data themselves. The data can be summarized by
clicking Statistics > Summaries, tables, and tests > Summary and
descriptive statistics > Summary statistics, and clicking the OK
button. You could also type summarize in the Command window and press
Enter. The result is a table containing summary statistics about all
the variables in the dataset:
. summarize |
Variable | Obs Mean Std. Dev. Min Max |
make
price
mpg
rep78
headroom | 0
74 6165.257 2949.496 3291 15906
74 21.2973 5.785503 12 41
69 3.405797 .9899323 1 5
74 2.993243 .8459948 1.5 5 |
trunk
weight
length
turn
displacement | 74 13.75676 4.277404 5 23
74 3019.459 777.1936 1760 4840
74 187.9324 22.26634 142 233
74 39.64865 4.399354 31 51
74 197.2973 91.83722 79 425 |
gear_ratio
foreign | 74 3.014865 .4562871 2.19 3.89
74 .2972973 .4601885 0 1 |
From this simple summary, we can learn a bit about the data. First of all,
the prices are nothing like today's car prices—of course, these cars
are now antiques. We can see that the gas mileages are not particularly good.
Automobile aficionados can gain some feel for other characteristics.
There are two other important items here:
- The variable make is listed as having no observations. It really
has no numerical observations, because it is a string (text) variable.
- The variable rep78 has 5 fewer observations than the other
numerical variables. This implies that rep78 has five missing values.
Although we could use the summarize and describe commands to get
a bird's eye view of the dataset, Stata has a command that gives a good
in-depth description of the structure, contents, and values of the variables:
the codebook command. Either type codebook in the Command
window and press Enter or navigate the menus to Data > Describe data >
Describe data contents (codebook) and click OK. We get a large
amount of output that is worth investigating. Look it over to see that much
can be learned from this simple command. You can scroll back in the Results
window to see earlier results, if need be. We'll focus on the output for
make, rep78, and foreign.
To start our investigation, we would like to run the codebook command
on just one variable, say, make. We can do this via menus or the
command line, as usual. To get the codebook output for make via
the menus, start by navigating as before to Data > Describe data >
Describe data contents (codebook). When the dialog appears, there are
multiple ways to tell Stata to consider only the make variable:
- We could type make into the Variables field.
- The Variables field is actually a combobox control that accepts
variable names. Clicking the button to the right of the Variables
field displays a list of the variables from the current dataset. Selecting
a variable from the list will, in this case, enter the variable name into
the edit field.
A much easier solution is to type codebook make in the Command window
and then press Enter. The result is informative:
. codebook make |
make Make and Model |
type: string (str18), but longest is str17
unique values: 74 missing "": 0/74
examples: "Cad. Deville"
"Dodge Magnum"
"Merc. XR-7"
"Pont. Catalina"
warning: variable has embedded blanks
|
The first line of the output tells us the variable name (make) and the
variable label (Make and Model). The variable is stored as a string
(which is another way of saying “text”) with a maximum length of
18 characters, though a size of only 17 characters would be enough. All the
values are unique, so, if need be, make could be used as an identifier
for the observations—something that is often useful when putting
together data from multiple sources or when trying to weed out errors from the
dataset. There are no missing values, but there are blanks within the makes.
This latter fact could be useful if we were expecting make to be a
single-word string variable.
Syntax note: telling the codebook command to run on
the make variable is an example of using a varlist in Stata's
syntax.
Looking at the foreign variable can teach us about value labels. We
would like to look at the codebook output for this variable, and, on the basis
of our latest experience, it would be easy to type codebook foreign into
the Command window to get the following output:
. codebook foreign |
foreign Car type |
type: numeric (byte)
label: origin
range: [0,1] units: 1
unique values: 2 missing .: 0/74
tabulation: Freq. Numeric Label
52 0 Domestic
22 1 Foreign
|
We can glean that foreign is an indicator variable, because its only
values are 0 and 1. The variable has a value label that displays
“Domestic” instead of 0 and “Foreign” instead of 1.
There are two advantages of storing the data in this form:
- Storing the variable as a byte takes less memory, because each
observation uses 1 byte instead of the 8 bytes needed to store
“Domestic”. This is important in large datasets. See [U]
12.2.2 Numeric storage types.
- As an indicator variable, it is easy to incorporate into statistical
models. See [U] 25.2 Using indicator variables in estimation.
Finally, we can learn a little about a poorly labeled variable with missing
values by looking at the rep78 variable. Typing codebook rep78
into the Command window yields
. codebook rep78 |
rep78 Repair Record 1978 |
type: numeric (int)
range: [1,5] units: 1
unique values: 5 missing .: 5/74
tabulation: Freq. Value
2 1
8 2
30 3
18 4
11 5
5 .
|
rep78 appears to be a categorical variable, but, because of lack of
documentation, we do not know what the numbers mean. (To see how we would
label the values, see chap. 10.) This variable has five missing values,
meaning that there are 5 observations for which the repair record is not
recorded. We can use the Data Browser to investigate these 5
observations—and we will do this using the Command window only. (Doing
so is much simpler.) If you recall from earlier, the command brought up by
clicking the Data Browser button was browse. We would like to browse
only those observations for which rep78 is missing, so we could type
. browse if missing(rep78)
From this, we see that the . entries are indeed missing
values—though other missing values are allowable. See [U] 12.2.1
Missing values. Close the Data Browser after you are satisfied with this
statement.
Syntax note: using the if qualifier above is what allowed us to look at
a subset of the observations.
Looking through the data lends us no clues about why these particular data are
missing. We decide to check the source of the data to see if the missing
values were originally missing or if they were omitted in error. Listing the
makes of the cars whose repair records are missing will be all we need,
because we saw earlier that the values of make are unique. This can
be done via the menus and a dialog.
- Select Data > Describe data > List data.
- Click the button to the right of the Variables field to show the
variable names.
- Click make to enter it into the Variables field.
- Click the by/if/in tab in the dialog.
- Type missing(rep78) into the If: (expression) box.
- Click Submit. Stata executes the proper command, but the dialog box
remains open. Submit is useful when experimenting, exploring, or
building complex commands. We will use primarily Submit in the
examples. You may click OK in its place if you like.
The same ends could be achieved by typing list make if missing(rep78).
The latter is easier, once you know that the command list is used for
listing observations. In any case, here is the output:
. list make if missing(rep78) |
| make |
3.
7.
45.
51.
64. | AMC Spirit
Buick Opel
Plym. Sapporo
Pont. Phoenix
Peugeot 604 |
We go to the original reference and find that the data were truly missing and
cannot be resurrected. See chapter 11 for more information about all that can
be done with the list command.
Syntax note: this command uses two new concepts for Stata commands—the
if qualifier and the missing() function. The if
qualifier restricts the observations the command runs to only those
observations for which the expression is true. See [U] 11.1.3 if exp.
The missing() function tests each observation to see if it is missing.
See [U] 13.3 Functions.
Now that we have a good idea about the underlying dataset, we can investigate
the data themselves.
Descriptive statistics
We saw above that the summarize command gave brief summary statistics
about all the variables. Suppose now that we became interested in the prices
while summarizing the data, because they seemed fantastically low (it was
1978, after all). To get an in-depth look at the price variable, we
can use the menus and a dialog:
- Select Statistics > Summaries, tables, and tests > Summary and
descriptive statistics > Summary statistics.
- Enter or select price in the Variables field.
- Select Display additional statistics.
- Click Submit.
Syntax note: as can be seen from the Results window, typing summarize
price, detail will get the same result. The portion after the comma
contains options for Stata commands; hence, detail is an example
of an option.
. summarize price, detail |
Price |
Percentiles Smallest
1% 3291 3291
5% 3748 3299
10% 3895 3667 Obs 74
25% 4195 3748 Sum of Wgt. 74
50% 5006.5 Mean 6165.257
Largest Std. Dev. 2949.496
75% 6342 13466
90% 11385 13594 Variance 8699526
95% 13466 14500 Skewness 1.653434
99% 15906 15906 Kurtosis 4.819188
|
From the output, we can see that the median price of the cars in the dataset
is only about $5,006! We could also see that the four most expensive cars are
all priced between $13,400 and $16,000. If we wished to browse the cars that
are the most expensive (and gain some experience with Stata's command syntax),
we could use an if qualifier,
. browse if price > 13000
and see from the Data Browser that the expensive cars are two Cadillacs and
two Lincolns, which have low gas mileage and are fairly heavy:
We now decide to turn our attention to foreign cars and repairs because, as we
glanced through the data, it appeared that the foreign cars had better repair
records. Let's start by looking at the proportion of foreign cars in the
dataset along with the proportion of cars with each type of repair record. We
can do this with one-way tables. The table for foreign cars can be
done via menus and a dialog starting with Statistics > Summaries, tables,
and tests > Tables > One-way tables and then choosing the variable
foreign in the Categorical variable field. Clicking
Submit yields
. tabulate foreign |
Car type |
Freq. Percent Cum. |
Domestic
Foreign |
52 70.27 70.27
22 29.73 100.00 |
Total |
74 100.00 |
We see that roughly 70% of the cars in the dataset are domestic, whereas 30%
are foreign made. The value labels are used to make the table so that the
output is nicely readable.
Syntax note: we also see that this one-way table could be made by using the
tabulate command together with a one variable: foreign.
Making a one-way table for the repair records is simple—it will be
simpler if done via the Command window. Typing tabulate rep78 yields
. tabulate rep78 |
Repair
Record 1978 |
Freq. Percent Cum. |
1
2
3
4
5 |
2 2.90 2.90
8 11.59 14.49
30 43.48 57.97
18 26.09 84.06
11 15.94 100.00 |
Total |
69 100.00 |
We can see that most cars have repair records of 3 and above, though the lack
of value labels makes us unsure what a “3” means. The five
missing values are indirectly evident, because the total number of
observations listed is 69 rather than 74.
These two one-way tables do not help us compare the repair records of foreign
and domestic cars. A two-way table would help greatly, which we can get by
using the menus and a dialog:
- Select Statistics > Summaries, tables, and tests > Tables > Two-way
tables with measures of association.
- Choose rep78 as the row variable.
- Choose foreign as the column variable.
- It would be nice to have the percentages within the foreign
variable, so check the Within-row relative frequencies checkbox.
- Click Submit.
Here is the resulting output.
. tabulate rep78 foreign, row |
Key |
frequency
row percentage |
Repair
Record
1978 |
Car type
Domestic Foreign |
Total |
1
| 2 0
100.00 0.00 |
2
100.00 |
2
|
8 0
100.00 0.00 |
8
100.00 |
3
|
27 3
90.00 10.00 |
30
100.00 |
4
|
9 9
50.00 50.00 |
18
100.00 |
5
|
2 9
18.18 81.82 |
11
100.00 |
Total
|
48 21
69.57 30.43 |
69
100.00 |
The output indicates that foreign cars are generally much better then domestic
cars when it comes to repairs. If you like, you could repeat the previous
dialog and try some of the hypothesis tests available from the dialog. We
will abstain.
Syntax note: we see that typing the command tabulate rep78 foreign, row
would have given us the same table. Thus using tabulate with two
variables yielded a two-way table. It makes sense that row is an
option. We went out of our way to check it in the dialog, so we
changed the behavior of the command from its default.
Continuing our exploratory tour of the data, we would like to compare gas
mileages between foreign and domestic cars, starting by looking at the summary
statistics for each group by itself. We know that a direct way to do this
would be to summarize mpg for each of the two values of foreign,
by using if qualifiers:
. summarize mpg if foreign==0 |
Variable |
Obs Mean Std. Dev. Min Max |
mpg |
52 19.82692 4.743297 12 34 |
. summarize mpg if foreign==1 |
Variable |
Obs Mean Std. Dev. Min Max |
mpg |
22 24.77273 6.611187 14 41 |
It appears that foreign cars get somewhat better gas mileage—we will
test this soon.
Syntax note: we needed to use a double equal sign (==) for testing
equality. This could be familiar to you if you have programmed before. If it
is unfamiliar, it is a common source of errors when initially using Stata.
Thinking of equality as “really equal” can cut down on typing
errors.
There are two other methods we could have used to produce these summary
statistics. These methods are worth knowing, because they are less error
prone. The first method duplicates the concept of what we just did by
exploiting Stata's ability run a command on each of a series of nonoverlapping
subsets of the dataset. To use the menus and a dialog, do the following:
- Select Statistics > Summaries, tables, and tests > Summary and
descriptive statistics > Summary statistics and click the Reset
button.
- Select mpg in the Variables field.
- Select Standard display option (if it is not already selected).
- Select the by/if/in tab.
- Check the Repeat command by groups checkbox.
- Select or type foreign for the grouping variable.
- Submit the command.
You can see that the results match those from above. They have a better
appearance because the value labels are used rather than the numerical values.
This method is more appealing because the results were produced without
knowing the possible values of the grouping variable ahead of time.
. by foreign, sort: summarize mpg |
-> foreign = Domestic
|
Variable |
Obs Mean Std. Dev. Min Max |
mpg | 52 19.82692 4.743297 12 34 |
| |
-> foreign = Foreign
|
Variable |
Obs Mean Std. Dev. Min Max |
mpg |
22 24.77273 6.611187 14 41 |
There is something different about the equivalent command that appears above:
it contains a prefix command called a by prefix. The by
prefix has its own option, namely, sort, to ensure that like members
are adjacent to each other before being summarized. The by prefix
command is important for understanding data manipulation and working with
subpopulations within Stata. Store this example away, and consult [U]
11.1.2 by varlist: and [U] 27.2 The by construct for more
information. Stata has other prefix commands for specialized treatment of
commands, as explained in [U] 11.1.10 Prefix commands.
The third method for tabulating the differences in gas mileage across the cars'
origins involves thinking about the structure of desired output. We need a
one-way table of automobile types (foreign versus domestic) within which we
see information about gas mileages. Looking through the menus yields the menu
item Statistics > Summaries, tables, and tests > Tables > One/two-way table
of summary statistics. Selecting this, entering foreign for
Variable 1 and mpg for the Summarize variable, and
submitting the command yields a nice table:
. tabulate foreign, summarize(mpg) |
Car type |
Summary of Mileage (mpg)
Mean Std. Dev. Freq. |
Domestic
Foreign |
19.826923 4.7432972 52
24.772727 6.6111869 22 |
Total |
21.297297 5.7855032 74 |
The equivalent command is evidently tabulate foreign, summarize(mpg).
Syntax note: this is a one-way table, so tabulate uses one variable.
The variable being summarized is passed to the tabulate command via an
option.
A simple hypothesis test
We would like to run a hypothesis test for the difference in the mean gas
mileages. Under the menus, Statistics > Summaries, tables, and tests >
Classical tests of hypotheses >Two-group mean-comparison test leads to the
proper dialog. Enter mpg for the Variable name and
foreign for the Group variable name, and then Submit the
dialog. The results are
. ttest mpg, by(foreign)
Two-sample t test with equal variances |
Group |
Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] |
Domestic
Foreign |
52 19.82692 .657777 4.743297 18.50638 21.14747
22 24.77273 1.40951 6.611187 21.84149 27.70396 |
combined |
74 21.2973 .6725511 5.785503 19.9569 22.63769 |
diff |
-4.945804 1.362162 -7.661225 -2.230384 |
diff = mean(Domestic) - mean(Foreign) t = -3.6308
Ho: diff = 0 degrees of freedom = 72
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
Pr(T < t) = 0.0003 Pr(|T| > |t|) = 0.0005 Pr(T > t) = 0.9997 |
From this, we could conclude that the mean gas mileage for foreign cars is
different from that of domestic cars (though we really ought to have tested
this before snooping through the data). We can also conclude that the
command, ttest mpg, by(foreign) is easy enough to remember. Feel free
to experiment with unequal variances, various approximations to the number of
degrees of freedom, and the like.
Syntax note: the by() option used here is not the same as the by
prefix command used earlier. Although it has a similar conceptual meaning,
its usage is different because it is a particular option for the ttest
command.
Descriptive statistics, correlation matrices
We now change our focus from exploring categorical relationships to exploring
numerical relationships: we would like to know if there is a correlation
between miles per gallon and weight. We select Statistics > Summaries,
tables, and tests > Summary and descriptive statistics > Correlations and
covariances in the menus. Entering mpg and weight, either
by clicking or typing, and then submitting the command yields
. correlate mpg weight
(obs=74)
|
| |
mpg weight |
mpg
weight |
1.0000
-0.8072 1.0000 |
The equivalent command for this is natural: correlate mpg weight.
There is a negative correlation, which is not surprising, because heavier cars
should be harder to push about.
We could see how the correlation compares for foreign and domestic cars by
using our knowledge of how the by prefix works. We can reuse the
correlate dialog or use the menus as before if the dialog is closed.
Click the by/if/in tab, check the Repeat command by groups
checkbox, and enter the foreign variable to define the groups. As done
above on page 19, a simple by foreign, sort: prefix in front of our
previous command would work, too:
. by foreign, sort: correlate mpg weight |
-> foreign = Domestic
(obs=52)
|
| |
mpg weight |
mpg
weight |
1.0000
-0.8759 1.0000 |
| |
-> foreign = Foreign
(obs=22)
|
| |
mpg weight |
mpg
weight |
1.0000
-0.6829 1.0000 |
We see from this that the correlation is not as strong among the foreign cars.
Syntax note: although we used the correlate command to look at the
correlation of two variables, Stata can make correlation matrices for an
arbitrary number of variables:
. correlate mpg weight length turn displacement
(obs=74)
|
| | mpg weight length turn displa~t |
mpg
weight
length
turn
displacement |
1.0000
-0.8072 1.0000
-0.7958 0.9460 1.0000
-0.7192 0.8574 0.8643 1.0000
-0.7056 0.8949 0.8351 0.7768 1.0000 |
This can be useful, for example, when investigating collinearity among
predictor variables. In fact, simply typing correlate will yield the
complete correlation matrix.
Graphing data
We have found several things in our investigations so far: We know the
average MPG of domestic and foreign cars differs. We have learned
domestic and foreign cars differ in other ways as well, such as in
frequency-of-repair record. We found a negative correlation of MPG and
weight—as we would expect—but the correlation appears stronger for
domestic cars.
We would now like to examine, with an eye toward modeling, the relationship
between MPG and weight, starting with a graph. We can start with a
scatterplot of mpg against weight. The command for this is
simple: scatter mpg weight. Using the menus requires a few steps
because the graphs in Stata can be customized heavily.
- Select Graphics > Twoway graph (scatter, line, etc.).
- Click the Create... button.
- Select the Basic plots radio button (if it is not already
selected).
- Select Scatter as the basic plot type (if it is not already
selected).
- Select mpg as the Y variable and weight as the
X variable.
- Click the Submit button.
The Results window shows the command issued from the menu:
. twoway (scatter mpg weight)
The command issued when the dialog was submitted is a bit more complex than
the command suggested above. There is good reason for this: the more
complex structure allows combining and overlaying graphs, as we will soon
see. In any case, the graph that appears is
We see the negative correlation in the graph, though the relationship appears
to be nonlinear.
Note: when you draw a graph, the Graph window appears, probably
covering up your Results window. Click on the main Stata window to get the
Results window back on top. Want to see the graph again? Click the
Graph button. See chapter 14 for more information about the
Graph button.
We would now like to see how the different correlations for foreign and
domestic cars are manifested in scatterplots. It would be nice to see a
scatterplot for each type of car, along with a scatterplot for all the data.
Syntax note: because we are looking at subgroups, this looks like it is a job
for by. We want one graph—think about whether it should be a
by() option or a by prefix.
Start as before:
- Select Graphics > Twoway graph (scatter, line, etc.) from the
menus.
- If Plot 1 is displayed under the Plot definitions and
(scatter mpg weight) appears below the Plot definitions box,
select it and skip to step 4.
- Go through the process to create the graph on the previous page.
- Click the By tab.
- Check the Draw subgraphs for unique values of variables checkbox.
- Enter foreign as the Variable.
- Check the Add a graph with totals checkbox.
- Click the Submit button.
The command and the associated graph are
. twoway (scatter mpg weight), by(foreign, total)
The graphs show that the relationship is nonlinear for both types of cars.
Syntax note: this is another use of a by() option. If you had used a
by prefix, two separate graphs would have been generated.
Model fitting: Linear regression
After looking at the graphs, we would like to fit a regression model that
predicts MPG from the weight and type of the car. From the graphs, the
relationship is nonlinear, so we will try modeling MPG as a quadratic in
weight. Also from the graphs, we judge the relationship to be different for
domestic and foreign cars. We will include an indicator (dummy) variable for
foreign and evalute afterward whether this adequately describes the
difference. Thus we will fit the model
mpg = β0 +
β1 weight +
β2
weight2 +
β3 foreign +
Î
foreign is already an indicator (0/1) variable, but we need to
create the weight-squared variable. This can be done via the menus, but
here using the command line is simpler:
. gen wtsq = weight^2
Now that we have all the variables we need, we can run a linear regression.
We’ll use the menus and see that the command is also simple. To use the
menus, select Statistics > Linear models and related > Linear
regression. In the resulting dialog, choose mpg as the dependent
variable and weight, wtsq, and foreign as the independent
variables. Submit the command. Here is the equivalent simple
regress command and the resulting analysis-of-variance table.
. regress mpg weight wtsq foreign |
Source |
SS df MS |
Model
Residual |
1689.15372 3 563.05124
754.30574 70 10.7757963 |
Total |
2443.45946 73 33.4720474 |
|
Number of obs = 74
F( 3, 70) = 52.25
Prob > F = 0.0000
R-squared = 0.6913
Adj R-squared = 0.6781
Root MSE = 3.2827
|
|
mpg |
Coef. Std. Err. t P>|t| [95% Conf. Interval] |
weight
wtsq
foreign
_cons |
-.0165729 .0039692 -4.18 0.000 -.0244892 -.0086567
1.59e-06 6.25e-07 2.55 0.013 3.45e-07 2.84e-06
-2.2035 1.059246 -2.08 0.041 -4.3161 -.0909002
56.53884 6.197383 9.12 0.000 44.17855 68.89913 |
|
The results look encouraging, so we will plot the predicted values on top of
the scatterplots for each of the types of cars. To do this, we need the
predicted, or fitted, values. This can be done via the menus, but doing it by
hand is simple enough. We will create a new variable mpghat:
. predict mpghat
(option xb assumed; fitted values)
The output from this command is simply a notification. Go over to the
Variables window and scroll to the bottom to confirm that there is now an
mpghat variable. If you try this command when mpghat
already exists, Stata will refuse to overwrite your data:
. predict mpghat
mpghat already defined
r(110);
The predict command, when used after a regression, is called a
postestimation command. As specified, it creates a new variable
called mpghat equal to
-.0165729weight + 1.59 * 10−6wtsq − 2.2035foreign + 56.53884
For careful model fitting, there are several features available to you after
estimation—one is calculating predicted values. Be sure to read [U]
20 Estimation and postestimation commands.
We can now graph the data and the predicted curve to evaluate the fit on the
foreign and domestic data separately to determine if our shift parameter is
adequate. We can draw both graphs together. Using the menus and a dialog, do
the following:
- Select Graphics > Twoway graph (scatter, line, etc.) from the
menus.
- If there are any plots listed, click the Reset button,
 .
- Create the graph for mpg versus weight.
- Click the Create... button.
- Be sure that Basic plots and Scatter are selected.
- Select mpg as the Y variable and weight as the
variable.
- Click Accept.
- Create the graph showing mpghat versus weight.
- Click the Create... button.
- Be sure that Basic plots and Line are selected.
- Select mpghat as the Y variable and weight as
the X variable.
- Check the Sort on x variable box. Doing so ensures that the
lines connect from smallest to largest weight values, instead of
the order in which the data happen to be.
- Click Accept.
- Show two plots, one each for domestic and foreign cars, on the same graph.
- Click the By tab.
- Check the Draw subgraphs for unique values of variables.
- Enter foreign in the Variables field.
- Click the Submit button.
Here are the resulting command and graph.
. twoway (scatter mpg weight) (line mpghat weight, sort), by(foreign)
Here we can see the reason for enclosing the separate scatter and
line commands in parentheses: they can then be overlaid by submitting
them together. The fit of the plots looks good and is cause for initial
excitement. So much excitement, in fact, that we decide to print the graph
and show it to an engineering friend. We print the graph, being careful to
print the graph and not all our results: File > Print from the Graph
window menu bar.
When we show our graph to our engineering friend, she is concerned.
“No,” she says. “It should take twice as much energy to move
2,000 pounds 1 mile compared with moving 1,000 pounds the same distance;
therefore, it should consume twice as much gasoline. Miles per gallon is not a
quadratic in weight; gallons per mile is a linear function of weight. Don't
you remember any physics?”
We try out what she says. We need to generate a gallons-per-mile variable and
make a scatterplot. Here are the commands we would need—note their
similarity to commands issued earlier in the session. There is one new
command: the label variable command, which allows us to give the
gpm variable a variable label so that the graph is labeled
nicely.
. generate gpm = 1/mpg
. label variable gpm "Gallons per mile"
. twoway (scatter gpm weight), by(foreign, total)
Sadly satisfied that the engineer is indeed correct, we rerun the regression:
. regress gpm weight foreign |
Source |
SS df MS |
Model
Residual |
.009117618 2 .004558809
.00284001 71 .00004 |
Total |
.011957628 73 .000163803 |
|
Number of obs = 74
F( 2, 71) = 113.97
Prob > F = 0.0000
R-squared = 0.7625
Adj R-squared = 0.7558
Root MSE = .00632 |
|
gpm |
Coef. Std. Err. t P>|t| [95% Conf. Interval] |
weight
foreign
_cons |
.0000163 1.18e-06 13.74 0.000 .0000139 .0000186
.0062205 .0019974 3.11 0.003 .0022379 .0102032
-.0007348 .0040199 -0.18 0.855 -.0087504 .0072807
|
|
We find that although foreign cars had better gas mileage than domestic cars
in 1978, it was because they were so light. In fact, according to our model
a foreign car with the same weight as a domestic car would use an additional
1/160 gallon per mile driven. With this, we are satisfied with our analysis.
Commands versus menus
In this chapter you have seen that Stata can operate either via menu choices
and dialog boxes or via the Command window. As you become more familiar with
Stata, you will find that the Command window is typically much faster for
often-used commands, whereas the menus and dialogs are faster when building up
complex commands such as graphs.
One of Stata's great strengths is the consistency of its command
syntax. Most of Stata's commands share the following syntax, where square
brackets mean that something is optional and a varlist is a list of
variables.
[prefix : ]
command
[varlist ]
[if ]
[in ]
[weight ]
[ , options ]
Some general rules:
- Most commands accept prefix commands that modify their behavior; see
[U] 11.1.10 Prefix commands for details. One of the more common
prefix commands is by.
- If an optional varlist is not specified, all the variables are
used.
- if and in restrict the observations on which the command
is run.
- options modify what the command does.
- Each command's syntax is found in the online help and the reference
manuals.
- Stata's command syntax includes more than we have shown you here, but
this should get you started. For more information, see [U] 11 Language
syntax and help language.
We saw examples using all the pieces of this except for the in
qualifier and the weight clause. The syntax for all commands can be
found in the online help along with examples—see chapter 6 for more
information. The explanation of the syntax can be found online using help
language. The consistent syntax makes it straightforward to learn new
commands and to read others' commands when examining an analysis.
Here is an example of reading the syntax diagram by using the summarize
command from earlier in this chapter. The syntax diagram for summarize
is typical:
summarize
[varlist ]
[if ]
[in ]
[weight ]
[ , options ]
This means that
| |
command by itself is valid: |
summarize |
| |
| |
command followed by a varlist (variable list) is valid: |
summarize mpg |
| |
|
summarize mpg weight |
| |
| |
command with if (with or without a varlist) is valid: |
summarize if mpg>20 |
| |
|
summarize mpg weight if mpg>20 |
| |
| |
and so on. |
|
You can learn about summarize in [R] summarize, or select
Help > Stata Command... and enter summarize, or type help
summarize in the Command window.
Keeping track of your work
It would have been useful if we had made a log of what we did so that we could
conveniently look back at interesting results or track any changes that were
made. You will learn to do this in chapter 16. Your logs will contain
commands and their output—another reason to learn command syntax, so
that you can remember what you've done.
To make a log file that keeps track of everything appearing in the Results
window, click the button that looks like a lab notebook,
 .
Choose a place to store your log file, and give it a name, just as you would
any other document. The log file will save everything that appears in the
Results window from the time you start a log file to the time that you close
it.
Conclusion
This chapter introduced you to Stata’s capabilities. You should now read and
work through the rest of this manual. Once you are done here, you can read
the User’s Guide.
See
New in Stata 12
for more about what was added in Stata Release 12.
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