11  Regression Analysis

11.1 Introduction

11.2 Simple Linear Regression

11.3 Multiple Linear Regression

11.4 Regression with Dummy Variables

11.5 Exercise

1. To understand the effectiveness of marketing investments, a manager of a company wants to analyze the relationship between marketing expenditures (USD) and the number of sales. Fit a simple linear regression model with marketing spend as the independent variable and sales as the dependent variable. Interpret the outputs. Note that, before fitting a regression model, it is essential to conduct an exploratory analysis.

Marketing expenditures (USD)	Number of Sales
100	522.3
115	596.2
120	617.7
132	682.3
144	740.2
154	792.5
158	806.4
160	813.5
170	871.0
180	920.6
181	927.9
190	968.5
200	1021.6
210	1068.2
220	1118.9
230	1171.2
240	1217.3
250	1272.1
260	1323.6
270	1369.6

2.To evaluate the association of marketing expenditures on sales, a company manager aims to analyze the relationship between marketing expenditures and sales across two different locations. Fit a multiple linear regression model with marketing expenditures and location as the independent variables and sales as the dependent variable. Interpret the outputs. Note that, before fitting a regression model, it is essential to conduct an exploratory analysis.

Marketing expenditures (USD)	Number of Sales	Location
100	522.3	A
115	596.2	A
120	617.7	A
132	682.3	A
144	740.2	A
154	792.5	A
158	806.4	A
160	813.5	A
170	871.0	A
180	920.6	A
181	927.9	A
190	968.5	A
200	1021.6	A
210	1068.2	A
220	1118.9	A
230	1171.2	A
240	1217.3	A
250	1272.1	A
260	1323.6	A
270	1369.6	A
100	522.3	B
115	596.2	B
120	617.7	B
132	682.3	B
144	740.2	B
154	792.5	B
158	806.4	B
160	813.5	B
170	871.0	B
180	920.6	B
181	927.9	B
190	968.5	B
200	1021.6	B
210	1068.2	B
220	1118.9	B
230	1171.2	B
240	1217.3	B
250	1272.1	B
260	1323.6	B
270	1369.6	B