In this problem, we aim to develop a predictive model to estimate the energy consumption of buildings equipped with HVAC $($Heating$,$ Ventilation, and Air Conditioning$)$ systems. The Dataset.csv contains information on various features that influence energy consumption in buildings. The goal is to leverage these features to accurately predict the energy usage $($in kilowatt$-$hours$)$ for different buildings. The table contains the following columns: Room Area $($sq$.$ ft$.)$

The area of the rooms in the building. Number of Appliances

The count of appliances present in each building. Outside Temperature $(\backslash$deg C$)$

The outside temperature recorded at each building's location. Insulation Thickness $($inches$)$

The thickness of insulation in the building's walls. Building Type

A categorical feature representing the type of building, such as residential or commercial. HVAC System

Another categorical feature representing the type of HVAC system installed in the building, such as Central AC$,$ Split AC$,$ or Window AC$.$ Average Temperature in last $24$ hours $(\backslash$deg C$)$

An additional numerical column highly correlated with the Outside Temperature, reflecting a similar trend in terms of impact on energy consumption. Energy Consumption $($kWh$)$

The output variable, representing the actual energy consumption $($in kilowatt$-$hours$)$ of each building based on the given features.

The objective of this problem is to build a predictive model that accurately estimates the energy consumption of buildings with HVAC systems. By leveraging the provided features, the model will predict the energy usage for new, unseen buildings, assisting homeowners, businesses, and energy providers in optimizing energy consumption and reducing costs.

Required Analysis:

a$)$

Determine the primary feature influencing energy consumption prediction? What about the secondary feature? Explain the reasons behind their significance.

b$)$

Identify any feature that may not contribute significantly to prediction accuracy. What is your mitigation strategy? If no such feature found, provide justification for your claim.

c$)$

Apply multiple linear regression to build a prediction model for energy consumption $($y$)$ based on the features. Feel free to modify the dataset to enhance prediction accuracy. Use the model to predict energy consumption for point$1,$ point$2,$ and point$3$: point $1$: Room Area $($sq$.$ ft$.)$: $279,$ Number of Appliances: $16,$ Outside Temperature $(\backslash$deg C$)$: $20,$ Insulation Thickness $($inches$)$: $1\mathrm{.}7,$ Building Type: Residential, HVAC System: Central AC$,$

Average Temperature in last $24$ hours $(\backslash$deg C$)$: $19,$ Energy Consumption $($kWh$)$: $385$

point $2$: Room Area $($sq$.$ ft$.)$: $277,$ Number of Appliances: $22,$ Outside Temperature $(\backslash$deg C$)$: $15,$

Insulation Thickness $($inches$)$: $1\mathrm{.}5,$ Building Type: Commercial, HVAC System: Split AC$,$

Average Temperature in last $24$ hours $(\backslash$deg C$)$: $14,$ Energy Consumption $($kWh$)$: $425$

point $3$: Room Area $($sq$.$ ft$.)$: $276,$ Number of Appliances: $14,$ Outside Temperature $(\backslash$deg C$)$: $25,$

Insulation Thickness $($inches$)$: $2\mathrm{.}2,$ Building Type: Residential, HVAC System: Window AC$,$

Average Temperature in last $24$ hours $(\backslash$deg C$)$: $26,$ Energy Consumption $($kWh$)$: $350$

d$)$

Compute the Mean Squared Error $($MSE$)$ regression loss using the "mean$\_$squared$\_$error" function from $$sklearn$.$metrics$$ library, for these points:

where y$\_$true is ground truth $($correct$)$ target values and y$\_$pred is estimated target values based on the linear regression model. $($Note that y$\_$true and y$\_$pred are vectors each containing three values corresponding to point$1,$ point$2,$ point$3.)$

e$)$

Given the following scatter plot of a new feature X with respect to Energy Consumption, recommend whether to include it in the features for prediction. Provide reason.

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$404550556065707580$

Energy Consumption

New Feature

Question $2$:

Consider the figure below where data points are divided into two classes, yellow circle, and blue square. Please answer the following questions:

a$)$

Draw the decision boundary for KNN$-$algorithm when K$=1.$

b$)$

How will the following points be classified by K$=3$ classifiers:

Prediction point $(8,6)$

Blue Square

Yellow Circle point $(8,4)$

Blue Square

Yellow Circle

Question $3$:

Given the following table where data points belong to two classes $-$ and $+.$ Using the KNN algorithm to predict the label $(+,-)$ for the following points:

$-$

point$1$: $(7\mathrm{.}81,5\mathrm{.}33)$

$-$

point$2$: $(9\mathrm{.}43,5\mathrm{.}29)$

a$)$

What is the predicted label $(+$ or $-)$ based on K$=3?$

b$)$

What is the index of the closest neighbors for each point?

Index X$1$ X$2$ Y

$1$

$8\mathrm{.}27$

$5\mathrm{.}59$

$+$

$2$

$1\mathrm{.}58$

$5\mathrm{.}87$

$-$

$3$

$5\mathrm{.}92$

$5\mathrm{.}87$

$-$

$4$

$9\mathrm{.}44$

$5\mathrm{.}83$

$+$

$5$

$2\mathrm{.}11$

$5\mathrm{.}57$

$-$

$6$

$4\mathrm{.}71$

$5\mathrm{.}94$

$+$

$7$

$3\mathrm{.}82$

$5\mathrm{.}84$

$+$

$8$

$6\mathrm{.}98$

$5\mathrm{.}91$

$-$

$9$

$3\mathrm{.}15$

$5\mathrm{.}42$

$-$

$10$

$8\mathrm{.}9$

$5\mathrm{.}94$

$-$

$11$

$7\mathrm{.}65$

$5\mathrm{.}77$

$+$

$12$

$9\mathrm{.}83$

$5\mathrm{.}29$

$-$

$13$

$1\mathrm{.}94$

$5\mathrm{.}36$

$+$

$14$

$7\mathrm{.}13$

$5\mathrm{.}28$

$-$

$15$

$5\mathrm{.}77$

$5\mathrm{.}47$

$-$

$16$

$4\mathrm{.}36$

$5\mathrm{.}31$

$+$

$17$

$5\mathrm{.}09$

$5\mathrm{.}65$

$-$

$18$

$3\mathrm{.}42$

$5\mathrm{.}24$

$+$

$19$

$2\mathrm{.}76$

$5\mathrm{.}71$

$+$

$20$

$9\mathrm{.}6$

$5\mathrm{.}52$

$-$

Delivery:

For the final submission, create tables like this and fill them with your results$/$answers:

Question $1$:

a$)$ primary fea