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Linear regression
Using linear regression, you can model the linear relationship between independent variables, or features, and a dependent variable, or outcome.
Using linear regression, you can model the linear relationship between independent variables, or features, and a dependent variable, or outcome. You can build linear regression models to:

Fit a predictive model to a training data set of independent variables and some dependent variable. Doing so allows you to use feature variable values to make predictions on outcomes. For example, you can predict the amount of rain that will fall on a particular day of the year.

Determine the strength of the relationship between an independent variable and some outcome variable. For example, suppose you want to determine the importance of various weather variables on the outcome of how much rain will fall. You can build a linear regression model based on observations of weather patterns and rainfall to find the answer.
Unlike Logistic regression, which you use to determine a binary classification outcome, linear regression is primarily used to predict continuous numerical outcomes in linear relationships.
You can use the following functions to build a linear regression model, view the model, and use the model to make predictions on a set of test data:
For a complete example of how to use linear regression on a table in Vertica, see Building a linear regression model.
1  Building a linear regression model
This linear regression example uses a small data set named faithful.
This linear regression example uses a small data set named faithful. The data set contains the intervals between eruptions and the duration of eruptions for the Old Faithful geyser in Yellowstone National Park. The duration of each eruption can be between 1.5 and 5 minutes. The length of intervals between eruptions and of each eruption varies. However, you can estimate the time of the next eruption based on the duration of the previous eruption. The example shows how you can build a model to predict the value of eruptions
, given the value of the waiting
feature.
Before you begin the example,
load the Machine Learning sample data.

Create the linear regression model, named linear_reg_faithful
, using the faithful_training
training data:
=> SELECT LINEAR_REG('linear_reg_faithful', 'faithful_training', 'eruptions', 'waiting'
USING PARAMETERS optimizer='BFGS');
LINEAR_REG

Finished in 6 iterations
(1 row)

View the summary output of linear_reg_faithful
:
=> SELECT GET_MODEL_SUMMARY(USING PARAMETERS model_name='linear_reg_faithful');

=======
details
=======
predictorcoefficientstd_err t_value p_value
++++
Intercept 2.06795  0.210639.81782 0.00000
waiting  0.07876  0.0029226.96925 0.00000
==============
regularization
==============
type lambda
+
none 1.00000
===========
call_string
===========
linear_reg('public.linear_reg_faithful', 'faithful_training', '"eruptions"', 'waiting'
USING PARAMETERS optimizer='bfgs', epsilon=1e06, max_iterations=100,
regularization='none', lambda=1)
===============
Additional Info
===============
Name Value
+
iteration_count  3
rejected_row_count 0
accepted_row_count 162
(1 row)

Create a table that contains the response values from running the PREDICT_LINEAR_REG
function on your test data. Name this table pred_faithful_results
. View the results in the pred_faithful_results
table:
=> CREATE TABLE pred_faithful_results AS
(SELECT id, eruptions, PREDICT_LINEAR_REG(waiting USING PARAMETERS model_name='linear_reg_faithful')
AS pred FROM faithful_testing);
CREATE TABLE
=> SELECT * FROM pred_faithful_results ORDER BY id;
id  eruptions  pred
++
4  2.283  2.8151271587036
5  4.533  4.62659045686076
8  3.6  4.62659045686076
9  1.95  1.94877514654148
11  1.833  2.18505296804024
12  3.917  4.54783118302784
14  1.75  1.6337380512098
20  4.25  4.15403481386324
22  1.75  1.6337380512098
.
.
.
(110 rows)
Calculating the mean squared error (MSE)
You can calculate how well your model fits the data using the MSE function. MSE returns the average of the squared differences between actual value and predicted values.
=> SELECT MSE (eruptions::float, pred::float) OVER() FROM
(SELECT eruptions, pred FROM pred_faithful_results) AS prediction_output;
mse  Comments
+
0.252925741352641  Of 110 rows, 110 were used and 0 were ignored
(1 row)
See also