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## Praxis Core Math

### Course: Praxis Core Math > Unit 1

Lesson 3: Statistics and probability- Data representations | Lesson
- Data representations | Worked example
- Center and spread | Lesson
- Center and spread | Worked example
- Random sampling | Lesson
- Random sampling | Worked example
- Scatterplots | Lesson
- Scatterplots | Worked example
- Interpreting linear models | Lesson
- Interpreting linear models | Worked example
- Correlation and Causation | Lesson
- Correlation and causation | Worked example
- Probability | Lesson
- Probability | Worked example

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# Interpreting linear models | Lesson

## What is a linear model?

If we graph data and notice a trend that is approximately linear, we can model the data with a

**line of best fit**. A line of best fit can be estimated by drawing a line so that the number of points above and below the line is about equal.While a line of best fit is not an exact representation of the actual data, it is a useful model that helps us interpret the data and make estimates.

### What skills are tested?

- Using a line of best fit to estimate values within or beyond the data shown
- Identifying the equation of a line of best fit
- Interpreting the slope of a line of best fit in a real world context

## How can we estimate a value within the data shown?

We can use a line of best fit to estimate a value within the data shown. Estimating a value means finding a y-value when given a specific x-value or finding an x-value when given a specific y-value on the line of best fit

To estimate a value

*within*the data shown, use the graph scales to locate the desired point on the line of best fit, and then estimate the other coordinate.## How can we estimate a value beyond the data shown?

We can use a line of best fit to estimate a value beyond the data shown. Estimating a value means finding a y-value when given a specific x-value or finding an x-value when given a specific y-value on the line of best fit.

To estimate a value

*beyond*the data shown, extend the graph scale and line of best fit to include the desired point and then estimate the value of the other coordinate.## How do we determine the equation of a line of best fit?

A line of best fit usually shows two key features.

- The
**y-intercept**, b, is the y-value when x, equals, 0. - The
**slope**, m, is the change in y when x increases by 1.

The equation for a line of best fit is: y, equals, m, x, plus, b, where left parenthesis, x, comma, y, right parenthesis represents any point that satisfies this equation.

## How do we interpret a linear model?

In context, the meaning of the slope and intercepts of the line of best fit must be explained with the appropriate units.

For example, suppose Paige collected data on how much time she spent on her phone and the percent battery life remaining. The scatterplot below shows the data and the line of best fit.

Using the points left parenthesis, 0, comma, 100, right parenthesis and left parenthesis, 13, comma, 0, right parenthesis, the slope of the line of best fit is about:

- This means that the
*battery life remaining*decreases by about 7, point, 7 percent for every additional hour of*time spent on phone*.

The y-intercept is about left parenthesis, 0, comma, 100, right parenthesis.

- This means when
*time spent on phone*is 0 hours, Paige has about 100 percent of*battery life remaining*.

The x-intercept is about left parenthesis, 13, comma, 0).

- This means when
*time spent on phone*is about 13 hours, Paige has about 0 percent of*battery life remaining*.

## Your turn!

## Things to remember

A line of best fit can be estimated by drawing a line so that the number of points above and below the line is about equal.

We can use a line of best fit to estimate values within or beyond the data shown.

- To estimate a value
*within*the data shown, use the graph scales to locate the desired point on the line of best fit, and then estimate the other coordinate. - To estimate a value
*beyond*the data shown, extend the graph scale and line of best fit to include the desired point, and then estimate the value of the other coordinate.

The equation for a line of best fit is: y, equals, m, left parenthesis, x, right parenthesis, plus, b, where left parenthesis, x, comma, y, right parenthesis represents any point which satisfies this equation.

- The
**y-intercept**, b, is the y-value when x, equals, 0. - The
**slope**, m, is the change in y when x increases by 1.

In context, the meaning of the slope of a line of best fit must be explained with the appropriate units.

- The slope specifies the change in y when x increases by 1.

## Want to join the conversation?

- This is very educational I dont have any questions(1 vote)
- How do you know which is the increase of money value and the increase of a rating for example?(1 vote)