- Create a linear model that describes a real-world situation
- Use linear regression to analyze a data set and find the best-fit line
- Calculate and use the coefficient of determination to determine how well a linear model fits the data
Practical Applications of Linear Models and Regression Analysis
In this ‘Apply It’ section, we delve into the practical world of linear models and regression analysis, essential tools in understanding and interpreting real-world data. From the sales trends of a local cafe to the population growth of a city, and even the graduation rates of high schools, you will explore how to construct and analyze linear models. These scenarios will not only enhance your analytical skills but also demonstrate the real-life significance of linear regression in various contexts.
Scenario 1: Local Cafe Sales Trend
You are given weekly sales data for a local cafe over the past year. Your task is to understand the sales trend and predict future sales.
| Week | Sales |
|---|---|
| 1 | [latex]500[/latex] |
| 2 | [latex]520[/latex] |
| 3 | [latex]540[/latex] |
| 4 | [latex]560[/latex] |
| 5 | [latex]580[/latex] |
| 6 | [latex]600[/latex] |
| 7 | [latex]620[/latex] |
| 8 | [latex]640[/latex] |
| 9 | [latex]660[/latex] |
| 10 | [latex]680[/latex] |
Having explored the commercial dynamics of a cafe, let’s broaden our perspective to a larger scale. In Scenario 2, you will analyze the population growth of an entire city. This shift from a business-focused scenario to urban development planning will challenge you to apply regression analysis to broader social trends, highlighting the versatility of these mathematical tools.
Scenario 2: City Population Growth
The city’s planning department has collected data on the city’s population growth over the past decade. They want to use this data for future urban development planning.
| Year | Population |
|---|---|
| 2010 | [latex]50,000[/latex] |
| 2011 | [latex]52,000[/latex] |
| 2012 | [latex]54,200[/latex] |
| 2013 | [latex]56,500[/latex] |
| 2014 | [latex]58,700[/latex] |
| 2015 | [latex]62,000[/latex] |
| 2016 | [latex]63,300[/latex] |
| 2017 | [latex]66,600[/latex] |
| 2018 | [latex]68,000[/latex] |
| 2019 | [latex]70,500[/latex] |