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R² Correlation

The coefficient of determination, often referred to as R² correlation or R-squared, is a statistical measure that assesses the goodness-of-fit of a regression model to the observed data. It quantifies the proportion of the variance in the dependent variable that can be explained by the independent variables in the model.
This document will describe how this tool can help assess the linear relationship between the data collected by a Sensorbee Device and the data collected by a reference station / device, by using the Pearson’s correlation coefficient (R²).

Steps:

  1. Select Device and Reference Station
      • In this step, you need to select following:
        • Type - refers to calibration type. Select “R² correlation”.
        • Installation - refers to your device installation
        • Gas Sensor - refers to the sensor you want to calibrate
        • Reference Station - refers to the reference station / device that contains the reference data of the targeted gas.
  1. Select the period to assess or compute the R² correlation.
      • Please make sure that both collected and reference data are available on the period that you select.
Figure 1 - Select a period
Figure 1 - Select a period
  1. Click Analyze button
      • If the selected period is final, click the “Analyze” button.
      Figure 2 - Analyze button
      Figure 2 - Analyze button
  1. Show Result
      • After clicking the “Analyze” button, the Pearson correlation coefficient graph will be shown.
Figure 3 - Pearson Correlation Graph
Figure 3 - Pearson Correlation Graph
  1. The graph includes the following details:
      • R² value
      Pearson correlation coefficient (r) value
      Strength
      Direction
      Greater than .5
      Strong
      Positive
      Between .3 and .5
      Moderate
      Positive
      Between 0 and .3
      Weak
      Positive
      0
      None
      None
      Between 0 and –.3
      Weak
      Negative
      Between –.3 and –.5
      Moderate
      Negative
      Less than –.5
      Strong
      Negative
      • The linear equation
        • Technical note: Linear regression is represented by an equation Y= BX + A. The B is the slope that is equal to r(Sy/Sx) where r is the correlation coefficient, Sy is the standard deviation of y values and Sx is the standard deviation of x value. The equation of A (the intercept) is equal to the meanY-(B*meanX), where meanY and meanX are the means of the y values and x values, respectively.
      • Significance of the Result
        • Using the Significance level of 0.001
          • p < 0.001 means the relationship is statistically significant.
          • p > 0.001 means the relationship is not statistically significant.