Regression in R - Assignment-15

Practice Problems: Regression in R

Problem 1: Simple Linear Regression – Predicting Electricity Consumption

Problem Statement

A household wants to study the relationship between the number of electrical appliances used per day and its daily electricity consumption.

The following data are collected:

Appliances Used	Electricity Consumption (Units)
2	8
3	11
4	14
5	17
6	19
7	23
8	26
9	29

Tasks

Using Simple Linear Regression in R:

1. Create a suitable data frame.
2. Build a linear regression model to predict electricity consumption based on the number of appliances used.
3. Obtain the regression equation.
4. Display the model summary.
5. Find the regression coefficients.
6. Calculate the predicted electricity consumption for a household using 10 appliances.
7. Obtain the predicted values and residuals.
8. Plot the actual observations and the fitted regression line.
9. Find and interpret the R-squared value.

---

Problem 2: Multiple Linear Regression – Predicting House Price

Problem Statement

A real estate company wants to predict the price of a house based on:

• Area of the house (square feet)
• Number of bedrooms

The following data are collected:

House	Area (sq. ft.)	Bedrooms	Price (Lakhs)
1	800	1	32
2	950	2	38
3	1100	2	45
4	1250	3	52
5	1400	3	58
6	1550	3	64
7	1700	4	72
8	1900	4	80
9	2100	4	88
10	2300	5	98

Tasks

Using Multiple Linear Regression in R:

1. Create a data frame containing the given data.
2. Build a multiple linear regression model to predict house price using:
   • Area
   • Number of bedrooms
3. Display the regression coefficients.
4. Obtain the detailed model summary.
5. Find the R-squared and Adjusted R-squared values.
6. Predict the price of a house having:
   • Area = 1800 sq. ft.
   • Bedrooms = 4
7. Obtain predicted values and residuals.
8. Create an Actual vs Predicted Price plot.
9. Interpret the contribution of the independent variables to the predicted house price.

---

Problem 3: Logistic Regression – Predicting Customer Purchase

Problem Statement

An online shopping company wants to predict whether a customer will purchase a product based on the amount of time spent browsing the website.

The outcome is represented as:

• 0 → Did Not Purchase
• 1 → Purchased

The following data are collected:

Customer	Browsing Time (Minutes)	Purchase
1	2	0
2	3	0
3	4	0
4	5	1
5	6	0
6	7	1
7	8	0
8	9	1
9	10	1
10	12	1
11	13	0
12	14	1
13	15	1
14	17	1
15	18	1

Tasks

Using Binary Logistic Regression in R:

1. Create a data frame containing the browsing time and purchase information.
2. Build a Logistic Regression model using browsing time as the predictor.
3. Display the model summary and interpret the regression coefficient.
4. Predict the probability of purchase for each customer.
5. Convert predicted probabilities into class labels using a 0.5 threshold.
6. Create a confusion matrix comparing actual and predicted classes.
7. Calculate the classification accuracy.
8. Predict whether a new customer who spends 11 minutes browsing is likely to purchase the product.
9. Plot the actual observations and the Logistic Regression probability curve.

---