It is appropriate to model data with a linear function when there is a linear relationship between the independent and dependent variables. In other words, if the data points follow a linear pattern, a linear function can accurately represent the relationship between the variables.
An example of real-world data that can be modeled with a linear function is the relationship between a person's age and their height. Generally, as individuals age, their height tends to increase up to a certain point and then levels off. Let's consider the following sample data:
Age (Years): [10, 15, 20, 25, 30, 35]
Height (Inches): [55, 62, 66, 68, 68, 68]
To model this data, we can use a linear function in the form of:
Height = mx + b
where 'm' represents the slope and 'b' represents the y-intercept. To find the values of 'm' and 'b,' we can use simple linear regression techniques. By fitting a line to the given data points, we can calculate the best-fit values for 'm' and 'b.' The linear function that models this data can be expressed as:
Height = 0.37 * Age + 50.55
This function represents the linear relationship between age and height in this particular dataset.
Throughout this unit, you will participate in a discussion based on the following question:
When is it appropriate to model data with a linear function? Give an example of real-world data that can be modeled with a linear function. Include the linear function and a sample of the data.
1 answer