Linear Regression on Combined Cycle Power Plant Data Set

source: www.hdwallpapers.in

Abstract: The data set contains 9568 data points collected from a Combined Cycle Power Plant over 6 years (2006–2011), when the plant was set to work with full load.

**Data Set Information: **The data set contains 9568 data points collected from a Combined Cycle Power Plant over 6 years (2006–2011), when the power plant was set to work with full load. Features consist of hourly average ambient variables Temperature (AT), Ambient Pressure (AP), Relative Humidity (RH) and Exhaust Vacuum (V) to predict the net hourly electrical energy output (PE) of the plant. A combined cycle power plant (CCPP) is composed of gas turbines (GT), steam turbines (ST) and heat recovery steam generators. In a CCPP, the electricity is generated by gas and steam turbines, which are combined in one cycle, and is transferred from one turbine to another. While the Vacuum is collected from and has effect on the Steam Turbine, the other three of the ambient variables effect the GT performance.

Attribute Information: Features consist of hourly average ambient variables

• *Avg Temperature (AT) in the range 1.81°C and 37.11°C,
• Ambient Pressure (AP) in the range 992.89–1033.30 millibar,
• Relative Humidity (RH) in the range 25.56% to 100.16%
• Exhaust Vacuum (V) in the range 25.36–81.56 cm Hg
• Net hourly electrical energy output (PE) 420.26–495.76 MW* The averages are taken from various sensors located around the plant that record the ambient variables every second. The variables are given without normalization.

Objective : Given the attributes we have to predict Net hourly electrical energy output (PE).

Code used for analysis and training the model can be found here

**Linear Regression**: this model makes prediction by simply computing a weighted sum of the input features, plus a constant called the intercept term.

Mathematically:- y^ = W0 X0+ W1 X1 + W2 X2 + ⋯ + Wn Xn

Where, y^ — > predicted output(Hypothesis function) ; Wi ‘s — > model parameters ( Weights ) ; n — > number of features and Xi ’s — > Features. Here X0 = 1.

source:https://duckduckgo.com/?t=ffab&q=linear+regression&iax=images&ia=images&iai=https%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2F4%2F41%2FLinearRegression.svg%2F1280px-LinearRegression.svg.png

The CCPP data set is clean, NO missing values and all are numerical attributes. So we are skipping IMPUTATION and FEATURE ENCODING(Categorical).

Exploratory Data Analysis (EDA): Histogram

Attribute Histogram plots

Observations:

• Ambient Pressure(AP) is Normally distributed
• Relative Humidity(RH) is Left Skewed
• The attribute scales are different

Scatter Matrix:

Correlation Matrix

Observations:

• Avg Temperature(AT) has strong -ve correlation with Net hourly electrical energy output (i.e PE) and is equal to -0.948
• Exhaust Vacuum(V) also has -ve correlation with PE and is equal to -0.869
• AP and RH have +ve correlation with PE.

After training Linear regression model I found the following parameters:

linreg.intercept, linreg.coef

(454.3457133524954, array([-14.76806055, -2.96077112, 0.38340356, -2.28983557]))

Learning curve:

Learning curve

Observations:

• The Validation error is decreasing over the iterations.
• Total cost is small. So model is neither OVERFITTING nor UNDERFITTING.

Try yourself:

• Polynomial Regression
• Different evaluation metric
• Solve using NORMAL EQUATION

Thanks for reading!! Happy learning :)