Principles of Managerial Statistics and Data Science

13Simple Linear Regression

13.1 Introduction

There is an immense amount of situations where one variable depends on another. For a given amount of money, the new balance in a bank account after a year is a function of the bank's interest rate. Similarly, the revenue of selling shirts at $12 a shirt is a function of the amount of shirts sold. Suppose the cost of a service is a linear function of usage of the service. For example, the monthly electricity bill may be

where is the amount to be paid, is the kilowatt‐hour for the month. 0.15 ¢ represents the cost per kilowatt‐hour. The equation tells us there is a basic monthly charge of $5. Hence, if a client is on vacation (and has unplugged everything) and consumed a total of 0 kWh, they must still pay $5 to the power company. If a client uses 100 kWh, their bill for the month should be . Figure 13.1 presents the association between power bill amount and kilowatt‐hour usage.

This example shows us that it is very convenient to express a variable as a function of another. If we know the kilowatt‐hours, cost per kilowatt‐hour and basic ...