Mathematical Models from Real-Life Data

Developing a mathematical model to represent real-world data will continue to be important in the study of calculus. Raw data is typically collected, graphed, analyzed, and interpreted in an effort to apply your findings to satisfy a question.

Scatter Plot

A scatter plot is a graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values. Scatter plots contain discrete points. View the video on creating scatter plots below.

Linear Regression Equation

Linear regression is an attempt to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered as the independent variable, and the other is considered as the dependent variable. A linear regression equation is of the form y = ax + b. Note that a is used instead of m, although the interpretation is identical.

View the video below to learn how to find a linear regression equation on a graphing calculator.

Mathematical Models from Real-Life Data

Given the following situation, create a scatter plot and find the linear regression equation (rounded to the nearest hundredth).

The distance required for a car to come to a complete stop is dependent upon the speed of the car at the time the driver makes the decision to stop. The reaction distance is the distance the car travels from the time the decision to stop is made until the moment the break is applied. Create a scatter plot of the speed (independent variable) versus reaction time (dependent variable). What is the equation that best fits this data?

Solution: y = .99x+6.48 text annotation indicator

image of car

Speed (mph)	Reaction Distance (ft)
20	22
30	40
40	48
50	55
60	66
70	74

Mathematical Models from Real-Life: Even More Problems

Complete problems from your textbook and/or online resources as needed to ensure your complete understanding of developing and interpreting mathematical models using scatter plots and linear regression equations.

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