Regression analysis seasonal 7.0
Summary
This operator calculates a regression model for a time series. The regression model tries to explain observations with the help of trends, seasonal variations and other influencing factors, and creates a forecast for future dates.
A time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals [1], e.g., temperature measured at every hour, or weekly sales figures.
The seasonal regression model allows also to analyze whether the observed data depend on other influencing factors (e.g., training, marketing campaigns, number of employees).
A detailed description of regression analysis methods can be found at [2].
Requirements for data to be analyzed
 Input data must be scaled, i.e., the time stamps in columns 'Date + time (from)' and 'Date + time (to)' represent uniform time intervals of the same duration. (see Scaling 8.0)
 Input data must be sorted by time stamps in the columns 'Date + time (from)' and 'Date + time (to)'.
 The columns 'Date + time (from)' and 'Date + time (to)' must not contain missing entries.
 The underlying data must comprise at least one complete season.
 If one or several observations are missing, the corresponding time stamps will be inserted into the data. The inserted entries are treated as missing observations.
Configuration
Input settings of existing table
Name 
Value 
Opt. 
Description 
Example 

Identifier 
System.Object 
opt. 
Columns by whose content the data is to be grouped. A separate regression analysis is performed for each group. 
 
Date + Time (from) 
System.DateTime 
 
Column containing the start times (date + time) of the observations. 
 
Date + Time (to) 
System.DateTime 
 
Column containing the end times (date + time) of the observations. 
 
Dinstinction column 
System.String 
opt. 
This column distinguishes observations from history from observations in the forecast period. Observations from history are marked with "H", observations in the forecast period with "F". This column only needs to be specified if the regression model contains an independent variable. 
 
Influencing factors 
System.Object 
opt. 
These columns represent those factors which influence the measured observations. The regression analysis tries to establish a (linear) relationship between these factors and the observations. These columns must not include more than one nonnumerical column, which contains precisely two different values. These two values are 01 coded. Note: more than one influencing factors are possible, values can be a double, e.g. representing the strength of the factor. Note: the sum of a subset of influecing factors must not be 1. E.g. 3 categories should be modeled in 2 factors. Following data properties potentially causes numeric problems:

 
Observations 
System.Double 
 
This (numeric) column contains the values, which have been observed in each interval of the time series on which the model is based. 
 
Settings
Name 
Value 
Opt. 
Description 
Example 

Duration of the season 
System.String

 
Please enter the duration of the season on which your data is based. 
52 weeks 
@BOXCOXTRANSFORMATION 
System.String

 
The BOXCOX transformation converts the observations into a form that can be used for the regression analysis. If you select 'automatic' as the type of BOXCOX transformation, a suitable transformation for the data on which the analysis is based is defined. Another type of transformation should then only be applied if you have sound knowledge of the data to be analysed. Select '1 (identity)', if the seasonal variations remain absolutely constant, e.g. the December value is always 1000 units higher than the annual average. Select '0 (logarithm)', if the seasonal variations are a constant percentage, e.g. the December value is always 20% higher than the annual average. Select '0.5 (root)', if the seasonal variations are a constant percentage, but the percentage rate reduces slightly over time, e.g. the first December value is 20% higher than the monthly average, the second December value is 19% higher, etc. Select '1 (reciprocal)' for nonnegative data with falling trend, for example, as for the sales data from a book shop, where high values are observed during the first few months after publications, but then fall with time. 
Automatic 
Forecast period 
System.Int32 
 
Please enter the period, e.g. the next 6 weeks, for which a forecast is to be calculated. 
26 
Time Unit 
System.String

 
Please enter the period, e.g. the next 6 weeks, for which a forecast is to be calculated. 
Weeks(s) 
Deliver as result 
System.String

 
Please select which data should be displayed in the results. 
Forecast + History 
Validate model over 
System.String

 
The observations are divided into a validation period and training period, e.g. validation period = the last 52 weeks of the data on which the model is based, training period = all other data. A regression model is created on the basis of the training period, and this model is used to estimate the data of the training and validation period. The percentage and average errors between the estimated and actual observations are determined for the training and validation period. If the errors for the training and validation period are very different, your regression model contains too many variables and returns inaccurate forecasts (overfitting). In this case, please try to simplify your model by removing one or more variables. 
Each forecast period 
Adjusted R² 
System.Double 
 
The adjusted determinacy, adj. R², provides information about the quality of a regression model, i.e. how well the regression model explains the data on which it is based. A value adj. R² = 0.95 means that 95% of the fluctuations in the data can be explained by the regression. Please enter in this field a minimum limit for the adj. R² of a regression model. If the adj. R² of a model exceeds this limit, the regression model is discarded and the forecast is created using the mean value of the data. 
0.6 
ANOVA pvalue 
System.Double 
 
Apart from the adjusted R², the p values of the ANOVA is another indicator of the quality of a regression model. High p values (e.g. larger than 0.1) indicate that the regression poorly explains the data on which it is based. Please enter an upper limit for the p value of the ANOVA. If this value is exceeded, the model is discarded and the forecasts are estimated using the mean value of the data. 
0.1 
p values (influencing factors) 
System.Double 
 
The p value of an independent variable provides information about whether the observations on which the data is based depends on any of these variables or not. Low values (e.g. less than 0.05) indicate a relationship between independent and dependent variables, high values on the other hand indicate that there are no relationships whatsoever. In this field, please enter a limit for the p value of a single independent variable. If the p value exceeds this limit, this variable will automatically be excluded from the regression model, provided you have activated 'excluded variables'. 
0.05 
Include seasonal variations 
System.String

 
The regression model tries to identify seasonal variations and to take these into account for the forecast. Note: danger of overfitting with strong 
middle 
Include intercept 
System.Boolean 
 
Please do not close the point of intersection unless you are really sure that it does not play any role in your observations. 
True 
Linear trend 
System.Boolean 
 
The regression model contains a linear trend, i.e. the observed values rise/fall linearly along the time axis. Note: wrong linear trend might occur due to extreme values in starting and ending of period, so try with and without linear trend 
True 
Include quadratic trend 
System.Boolean 
 
The regression model contains a quadratic trend, i.e. the observed values rise/fall quadratically along the time axis. 
False 
Include logarithmic trend 
System.Boolean 
 
The regression model contains logarithmic trend, i.e. the observed values rise/fall logarithmically along the time axis. 
False 
Include day in year 
System.Boolean 
 
The location of a date within the year is taken into account in the regression model, e.g. 3.1.2010 is the third day of the year. 
False 
Include day in month 
System.Boolean 
 
The location of a date within the month is taken into account in the regression model , e.g. 3.1.2010 is the third day in January. 
False 
Include day in week 
System.Boolean 
 
The effect of different week days is taken into account in the regression model. 
False 
Include quarters 
System.Boolean 
 
Quarterly periods are taken into account in the regression model. 
False 
Summer time 
System.Boolean 
 
Summer time is taken into account in the regression model. 
False 
Include previous time interval 
System.Boolean 
 
The regression analysis examines, whether observations in your previous observations are affected in the scale. 
False 
Include previous day 
System.Boolean 
 
The regression analysis examines whether observations are affected by the observations on the previous day. 
False 
Previous week 
System.Boolean 
 
The regression analysis examines whether observations are affected by the observations in the previous week. Note: may easily lead to exponential growth, so disable in doubt. 
False 
Previous year 
System.Boolean 
 
The regression analysis examines whether observations are affected by the observations in the previous year. 
False 
Exclude insignificant influencing factors 
System.Boolean 
 
Influencing factors whose p values exceed the limit given in the 'p values field (influencing factors)' will be excluded from the regression model. Note: starting from full model and iteratively exclude factor with highest p value greater than threshold 
True 
Ignore 0 values 
System.Boolean 
 
Rows with 0 values are ignored and are treated like missing data. 
False 
Output the validation result in data nodes 
System.Boolean 
 
If selected, the validation results are displayed in a separate data node. 
False 
Output error messages/warnings in data nodes 
System.Boolean 
 
If selected, error messages and warnings are displayed in a separate data node. 
False 
Remarks
 Additional information, such as training and validation errors, and warnings, are reported in the description field of the operation within the TISGUI.
 If the column of an influencing factor contains the same constant value for each observation no regression analysis can be carried out. Thus, constant factors are excluded automatically.
Want to learn more?
This operator calculates a regression model for a time series. The regression model tries to explain observations with the help of trends, seasonal variations and other influencing factors, and creates a forecast for future dates.
Examples
Example: Regression model with trend and season
Situation 
We consider the number of incoming phone calls at a call center over a time period. We are given the number of incoming calls for each week during the last four years.


Settings 

Result 
The result table shows the forecast (G), and the lower and upper limits of the confidence intervals (E and F).
By adding a chart operation Chart: Histogram Time Pattern the visualization shows that the historical forecasts (orange line) estimated with the obtained regression model show a similar trend and seasonal behaviour as the historic observations (blue line). The red line shows the estimated number of phone calls for the next 52 weeks.

ProjectFile 
Example: Regression model with trend, season and influencing factors
Situation 
On the basis of that modified input we can now build an extended regression model. We specify advertising campaigns as an addtional influencing factor and the distinction column in the settings of the regression operation. 

Settings 

Result 
The resulting data node shows the forecast (G), and the lower and upper CI limits (E, F).
In the histogram visualizing the results (added with the operation Chart: Histogram Time Pattern) we see that campaigns could indeed explain an increased number of incoming calls in the past (compare orange and blue line). Also the forecast for the next 52 weeks (red line) contains high values whenever an advertising campaign will be run.

Example: Comparison of different regression models
Situation 
To be able to compare two or several regression models with each other, operation regression analysis 6.0 validates each model in the following manner.


Settings 

Result 
If we consider and compare the validation error associated with the two models from example 1 and example 2 we see that the validation error could be reduced by including advertising campaigns within the model for example 2.  In general, one regression model should be preferred against the other only if it has a significantly lower validation error. 
Troubleshooting
Problem 
Frequent Cause 
Solutions 

Error message: "Object reference not set to an instance of an object." 
in TIS 5.8.2, this error message occurs when the box "Output the validation result in data nodes" is checked. This is a bug, see ticket FLEX505  Regressionsanalyse 6.0  Fehler Validierung AUCH in Regression Open

 
Forecast for excluded days, e.g., holiday. 
The operator does not consider if a day in the future period is a day to be excluded or not. In our TIS Forecast solution not additional influcencing factors for days to be exlcuded are provided. If a regression model is based on at least of these influencing factor, the forecasted value for that day will be null. If a regression model does not use any additional influencing factors, e.g., they are all elminated due a high pvalue, then will be a forecasted value for an excluded day. 
In the TIS forecasting solution those forecasted rows representing excluded days will be eliminated after the regression forecast (merge data, rows without a common key in data node 2). 