Regression on Airfoil Self-Noise dataset using Linear Regression approach

This case study using Airfoil Self-Noise dataset.

The NASA data set comprises different size NACA 0012 airfoils at various wind tunnel speeds and angles of attack. The span of the airfoil and the observer position were the same in all of the experiments.

The columns in this dataset are:

  1. A = Frequency
  2. B = Angle of attack
  3. C = Chord length
  4. D = Free-stream velocity
  5. E = Suction side displacement thickness
  6. F = Scaled sound pressure level

Sample Airfoil Self-Noise data

Sample Airfoil Self-Noise data

Sample Airfoil Self-Noise data

Prediction variables (attributes)

  1. Frequency, in Hertzs.
  2. Angle of attack, in degrees.
  3. Chord length, in meters.
  4. Free-stream velocity, in meters per second.
  5. Suction side displacement thickness, in meters.

Target variables

  1. Scaled sound pressure level, in decibels.
shape of the DataFrame

shape of the DataFrame

There are 1503 observations in the dataset.

Scatter plots

Scatter plots

Use Statsmodels to estimate the model coefficients for the Airfoil Self-Noise data with B (angle of attack):

model coefficients for the Airfoil Self-Noise data

model coefficients for the Airfoil Self-Noise data

Interpreting Model Coefficients

Interpretation angle of attack coefficient (β1)

  • A “unit” increase in angle of attack is associated with a 0.008927 “unit” increase in F (scaled sound pressure level).

Using the Model for Prediction

Let’s say that where the Angle of attack increased was 70. What would we predict for the scaled sound pressure level? (First approach for prediction)

126.309388 + (0.008927 * 70) = 126.934278

Thus, we would predict scaled sound pressure level of 126.934278.

Use Statsmodels to make the prediction: (Second approach for prediction)

Statsmodels to make the prediction

Statsmodels to make the prediction

Plotting the Least Squares Line

Make predictions for the smallest and largest observed values of x, and then use the predicted values to plot the least squares line:

DataFrame with the minimum and maximum values of B

DataFrame with the minimum and maximum values of B

 

predictions for those x values

predictions for those x values

least squares line

least squares line

 

confidence intervals for the model coefficients

confidence intervals for the model coefficients

2 thoughts on “Regression on Airfoil Self-Noise dataset using Linear Regression approach

  1. Really interesting take on airfoil self noise data… I may try to play around it myself. However, it would really have been great to see your Python code and not just the output and visualisations. I came here for some code.

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