## Description

## 1. Combined Cycle Power Plant Data Set

The dataset contains 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 (T), Ambient Pressure (AP),

Relative Humidity (RH) and Exhaust Vacuum (V) to predict the net hourly electrical

energy output (EP) of the plant.

(a) Download the Combined Cycle Power Plant data1

from:

https://archive.ics.uci.edu/ml/datasets/Combined+Cycle+Power+Plant

(b) Exploring the data:

i. How many rows are in this data set? How many columns? What do the rows

and columns represent?

ii. Make pairwise scatterplots of all the varianbles in the data set including the

predictors (independent variables) with the dependent variable. Describe

your findings.

iii. What are the mean, the median, range, first and third quartiles, and interquartile ranges of each of the variables in the dataset? Summarize them

in a table.

(c) For each predictor, fit a simple linear regression model to predict the response.

Describe your results. In which of the models is there a statistically significant

association between the predictor and the response? Create some plots to back

up your assertions. Are there any outliers that you would like to remove from

your data for each of these regression tasks?

(d) Fit a multiple regression model to predict the response using all of the predictors.

Describe your results. For which predictors can we reject the null hypothesis

H0 : βj = 0?

(e) How do your results from 1c compare to your results from 1d? Create a plot

displaying the univariate regression coefficients from 1c on the x-axis, and the

multiple regression coefficients from 1d on the y-axis. That is, each predictor is

displayed as a single point in the plot. Its coefficient in a simple linear regression

model is shown on the x-axis, and its coefficient estimate in the multiple linear

regression model is shown on the y-axis.

(f) Is there evidence of nonlinear association between any of the predictors and the

response? To answer this question, for each predictor X, fit a model of the form2

Y = β0 + β1X + β2X

2 + β3X

3 +

(g) Is there evidence of association of interactions of predictors with the response? To

answer this question, run a full linear regression model with all pairwise interaction

terms and state whether any interaction terms are statistically significant.

1There are five sheets in the data. All of them are shuffled versions of the same dataset. Work with Sheet

1.

2https://scikit-learn.org/stable/modules/preprocessing.htm\#generating-polynomial-features

(h) Can you improve your model using possible interaction terms or nonlinear associations between the predictors and response? Train the regression model on a

randomly selected 70% subset of the data with all predictors. Also, run a regression model involving all possible interaction terms and quadratic nonlinearities,

and remove insignificant variables using p-values (be careful about interaction

terms). Test both models on the remaining points and report your train and test

MSEs.

(i) KNN Regression:

i. Perform k-nearest neighbor regression for this dataset using both normalized

and raw features. Find the value of k ∈ {1, 2, . . . , 100} that gives you the

best fit. Plot the train and test errors in terms of 1/k.

(j) Compare the results of KNN Regression with the linear regression model that has

the smallest test error and provide your analysis.

2. ISLR: 2.4.1

3. ISLR: 2.4.7