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Linear regression is a technique used to investigate if and how a variable is linearly related to others. If a variable is found to be linearly related, then this can be used to predict future values of that variable.

In example Example 5.7, the service department of the company wanted to
be able to predict the time to repair equipment, in order to improve
the accuracy of their quotations.
It was suggested that the time to repair might be related to the time
between failures and the duty cycle of the equipment.
The p-value of 0.1 was chosen for this investigation.
In order to investigate this hypothesis, the `REGRESSION`

command
was used.
This command not only tests if the variables are related, but also
identifies the potential linear relationship. See REGRESSION.

PSPP> get file='/usr/local/share/pspp/examples/repairs.sav'. PSPP> regression /variables = mtbf duty_cycle /dependent = mttr. PSPP> regression /variables = mtbf /dependent = mttr. Output (excerpts): Coefficients (Mean time to repair (hours) ) +------------------------+-----------------------------------------+-----+----+ | | Unstandardized Standardized | | | | | Coefficients Coefficients | | | | +---------+-----------+-------------------+ | | | | B | Std. Error| Beta | t |Sig.| +------------------------+---------+-----------+-------------------+-----+----+ |(Constant) | 9.81| 1.50| .00| 6.54|.000| |Mean time between | 3.10| .10| .99|32.43|.000| |failures (months) | | | | | | |Ratio of working to non-| 1.09| 1.78| .02| .61|.552| |working time | | | | | | +------------------------+---------+-----------+-------------------+-----+----+ Coefficients (Mean time to repair (hours) ) +-----------------------+------------------------------------------+-----+----+ | | Unstandardized Standardized | | | | | Coefficients Coefficients | | | | +---------+------------+-------------------+ | | | | B | Std. Error | Beta | t |Sig.| +-----------------------+---------+------------+-------------------+-----+----+ |(Constant) | 10.50| .96| .00|10.96|.000| |Mean time between | 3.11| .09| .99|33.39|.000| |failures (months) | | | | | | +-----------------------+---------+------------+-------------------+-----+----+ |

The coefficients in the first table suggest that the formula
* mttr = 9.81 + 3.1 \times mtbf + 1.09 \times duty_cycle*
can be used to predict the time to repair.
However, the significance value for the

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