ID - Linear Regression (Lesson)

Linear Regression

The table shows the median age of females living in the U.S. based on the results of the U.S. Census over the past few decades.

Year

Median Age of Females

1970

29.2

1980

31.3

1990

34.0

2000

36.5

2010

38.2

Let's consider time to be the independent variable and the age as the dependent variable.

Let's take a look at the scatter plot that would represent this data:

Median age of females graph

Since the data points appear to be linear in shape, we want to find a linear model that represents the data. We do that by drawing a line of best fit. A line of best fit is a line that passes as close as possible to the plotted points, but it does not necessarily have to pass through any or all of them. The line should try to go in between or through as many points as possible.   

 

Let's use the equation we got from the calculator a(t) = 0.2x + 29.2 to make a prediction about the median age of U.S. females in 2020.

Step 1: 2020 is 50 years after 1970, so let t = 50

Step 2: Substitute into your equation:

a(50) = 0.2(50) + 29.2

a(50) = 10.29.2

a(50) = 39.2

So we can predict the median age of females in the U.S. in 2020 might be around 39.2

Using Technology

You can use a calculator or desmos.com to find a linear regression line. Every calculator differs in how this works. Find the model name and number of your calculator and search for the instructions on how to find a linear regression line. This video will demonstrate how to use desmos to determin a linear regression line.

Linear Regression Practice

Determine a linear equation that best represents the table of values. Create a scatterplot and draw in the line of best fit. Then, determine the slope and the intercept of that line to create the equation.  Complete at least one by hand and for the others, you can use your calculator or desmos.com.

1.

TableOne.png

2.

TableTwo.png

3.

TableThree.png

Using the linear model relating the time since 1970 and the median age of U.S. females, a(t) = 0.2x + 29.2, answer the questions below:

4. Approximate the median age of U.S. females in 2015.                   

5. When will the approximate age of U.S. females be 42? 

TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.

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