Predicting flight delays with regression analysis

Each document in the data set contains details for a single flight, so this data is ready for analysis; it is already in a two-dimensional entity-based data structure. In general, you often need to transform the data into an entity-centric index before you analyze the data.

In order to be analyzed, a document must contain at least one field with a supported data type (numeric, boolean, text, keyword or ip) and must not contain arrays with more than one item. If your source data consists of some documents that contain the dependent variable and some that do not, the model is trained on the subset of the documents that contain it.

{
  "_index": "kibana_sample_data_flights",
  "_type": "_doc",
  "_id": "S-JS1W0BJ7wufFIaPAHe",
  "_version": 1,
  "_seq_no": 3356,
  "_primary_term": 1,
  "found": true,
  "_source": {
    "FlightNum": "N32FE9T",
    "DestCountry": "JP",
    "OriginWeather": "Thunder & Lightning",
    "OriginCityName": "Adelaide",
    "AvgTicketPrice": 499.08518599798685,
    "DistanceMiles": 4802.864932998549,
    "FlightDelay": false,
    "DestWeather": "Sunny",
    "Dest": "Chubu Centrair International Airport",
    "FlightDelayType": "No Delay",
    "OriginCountry": "AU",
    "dayOfWeek": 3,
    "DistanceKilometers": 7729.461862731618,
    "timestamp": "2019-10-17T11:12:29",
    "DestLocation": {
      "lat": "34.85839844",
      "lon": "136.8049927"
    },
    "DestAirportID": "NGO",
    "Carrier": "ES-Air",
    "Cancelled": false,
    "FlightTimeMin": 454.6742272195069,
    "Origin": "Adelaide International Airport",
    "OriginLocation": {
      "lat": "-34.945",
      "lon": "138.531006"
    },
    "DestRegion": "SE-BD",
    "OriginAirportID": "ADL",
    "OriginRegion": "SE-BD",
    "DestCityName": "Tokoname",
    "FlightTimeHour": 7.577903786991782,
    "FlightDelayMin": 0
  }
}

To predict the number of minutes delayed for each flight:

Now you have a new index that contains a copy of your source data with predictions for your dependent variable.

When you view the regression results in Kibana, it shows the contents of the destination index in a tabular format:

In this example, the table shows a column for the dependent variable (FlightDelayMin), which contains the ground truth values that we are trying to predict with the regression analysis. It also shows a column for the prediction values (ml.FlightDelayMin_prediction) and a column that indicates whether the document was used in the training set (ml.is_training). You can filter the table to show only testing or training data and you can select which fields are shown in the table.

If you do not use Kibana, you can see the same information by using the standard Elasticsearch search command to view the results in the destination index.

GET df-flight-delays/_search

          ...
          "DestRegion" : "UK",
          "OriginAirportID" : "LHR",
          "DestCityName" : "London",
          "FlightDelayMin" : 66,
          "ml" : {
            "FlightDelayMin_prediction" : 62.527,
            "is_training" : false
          }
          ...

Though you can look at individual results and compare the predicted value (ml.FlightDelayMin_prediction) to the actual value (FlightDelayMins), you typically need to evaluate the success of the regression model as a whole.

Kibana provides training error metrics, which represent how well the model performed on the training data set. It also provides generalization error metrics, which represent how well the model performed on testing data.

A mean squared error (MSE) of zero means that the models predicts the dependent variable with perfect accuracy. This is the ideal, but is typically not possible. Likewise, an R-squared value of 1 indicates that all of the variance in the dependent variable can be explained by the feature variables. Typically, you compare the MSE and R-squared values from multiple regression models to find the best balance or fit for your data.

For more information about the interpreting the evaluation metrics, see Regression evaluation.

You can alternatively generate these metrics with the data frame analytics evaluate API.

POST _ml/data_frame/_evaluate
{
 "index": "df-flight-delays",   
  "query": {
      "bool": {
        "filter": [{ "term":  { "ml.is_training": true } }]  
      }
    },
 "evaluation": {
   "regression": {
     "actual_field": "FlightDelayMin",   
     "predicted_field": "ml.FlightDelayMin_prediction", 
     "metrics": {
       "r_squared": {},
       "mean_squared_error": {}
     }
   }
 }
}

{
  "regression" : {
    "mean_squared_error" : {
      "error" : 3006.517622042659
    },
    "r_squared" : {
      "value" : 0.6794200914263231
    }
  }
}

POST _ml/data_frame/_evaluate
{
 "index": "df-flight-delays",
  "query": {
      "bool": {
        "filter": [{ "term":  { "ml.is_training": false } }] 
      }
    },
 "evaluation": {
   "regression": {
     "actual_field": "FlightDelayMin",
     "predicted_field": "ml.FlightDelayMin_prediction",
     "metrics": {
       "r_squared": {},
       "mean_squared_error": {}
     }
   }
 }
}

If you don’t want to keep the data frame analytics job, you can delete it. For example, use Kibana or the delete data frame analytics job API. When you delete data frame analytics jobs, the destination indices remain intact.