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Practical 06 1044 1-1

This document outlines a practical project on multiple linear regression using a housing dataset to analyze the relationship between house prices and factors like average number of rooms, low-income population percentage, and pupil-teacher ratio. It includes steps for data creation, model fitting in R, and visualizations to interpret results and evaluate model performance. The project emphasizes the unique influence of each independent variable on the dependent variable, MEDV (median home value).

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rahulparande20
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38 views3 pages

Practical 06 1044 1-1

This document outlines a practical project on multiple linear regression using a housing dataset to analyze the relationship between house prices and factors like average number of rooms, low-income population percentage, and pupil-teacher ratio. It includes steps for data creation, model fitting in R, and visualizations to interpret results and evaluate model performance. The project emphasizes the unique influence of each independent variable on the dependent variable, MEDV (median home value).

Uploaded by

rahulparande20
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Practical 05: MULTIPLE REGRESSION MODEL

AIM: MULTIPLE REGRESSION MODEL Apply multiple regressions, if data have a continuous
independent variable.
Multiple Regression model:

Multiple Linear Regression is a statistical technique that models the relationship between one
dependent variable and two or more independent variables.It helps answer questions like:

Description:

In this project, we use a small custom housing dataset to understand the relationship
between house prices and other influencing factors. The dependent variable is MEDV
(median home value), and independent variables are:

 RM — Average number of rooms


 LSTAT — Percentage of low-income population
 PTRATIO — Pupil-teacher ratio

In this project, we use a small custom housing dataset to understand the relationship
between house prices and other influencing factors. The dependent variable is MEDV
(median home value), and independent variables are:

 RM — Average number of rooms


 LSTAT — Percentage of low-income population
 PTRATIO — Pupil-teacher ratio
A) Multiple regression:

Code:

# Step 1: Create the dataset

price <- c(24, 21, 34, 19, 28, 23, 17, 31, 26, 22)

rooms <- c(6.5, 5.8, 7.0, 5.3, 6.8, 6.1, 5.5, 7.2, 6.3, 5.9)

low_income <- c(12.0, 15.5, 5.0, 20.0, 8.5, 13.0, 22.0, 6.0, 10.0, 14.0)

ptratio <- c(18.0, 20.0, 16.5, 21.0, 17.0, 19.5, 22.0, 16.0, 18.5, 20.0)

# Step 2: Combine into a dataframe

housing <- data.frame(

MEDV = price,

RM = rooms,

LSTAT = low_income,

PTRATIO = ptratio

# Step 3: Build the multiple linear regression model

model <- lm(MEDV ~ RM + LSTAT + PTRATIO, data = housing)

# Step 4: Summary of the model

summary(model)

# Step 5: Plotting

# Plot 1: RM vs MEDV with regression line

plot(housing$RM, housing$MEDV, main="Rooms vs Price",

xlab="Average Number of Rooms", ylab="Price (MEDV)", pch=19, col="blue")

abline(lm(MEDV ~ RM, data = housing), col="red", lwd=2)

# Plot 2: LSTAT vs MEDV

plot(housing$LSTAT, housing$MEDV, main="% Low Income vs Price",

xlab="% Lower Status Population", ylab="Price (MEDV)", pch=19, col="darkgreen")

# Plot 3: PTRATIO vs MEDV

plot(housing$PTRATIO, housing$MEDV, main="Pupil-Teacher Ratio vs Price",

xlab="PTRATIO", ylab="Price (MEDV)", pch=19, col="purple")


# Plot 4: Residuals plot

plot(model$residuals, main="Residuals Plot", ylab="Residuals", pch=19, col="orange")

abline(h=0, col="red", lty=2)

OUTPUT:

✅ Learnings

Through this project, I learned how to apply multiple linear regression in R to predict
outcomes using multiple variables. I gained hands-on experience with data creation, model
fitting using lm(), and result interpretation using R output. I also learned how to visualize
relationships and residuals to evaluate model performance. Lastly, I understood how each
independent variable uniquely influences the dependent variable in a multivariate context.

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