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## Statistics and probability

### Unit 5: Lesson 3

Introduction to trend lines- Fitting a line to data
- Estimating the line of best fit exercise
- Eyeballing the line of best fit
- Estimating with linear regression (linear models)
- Estimating equations of lines of best fit, and using them to make predictions
- Line of best fit: smoking in 1945
- Estimating slope of line of best fit
- Equations of trend lines: Phone data
- Linear regression review

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# Linear regression review

Linear regression is a process of drawing a line through data in a scatter plot. The line summarizes the data, which is useful when making predictions.

### What is linear regression?

When we see a relationship in a scatterplot, we can use a line to summarize the relationship in the data. We can also use that line to make predictions in the data. This process is called

**linear regression**.*Want to see an example of linear regression? Check out this video.*

### Fitting a line to data

There are more advanced ways to fit a line to data, but in general, we want the line to go through the "middle" of the points.

*Want to learn more about fitting a line to data? Check out this video.*

*Want to practice more problems like this? Check out this exercise.*

### Using equations for lines of fit

Once we fit a line to data, we find its equation and use that equation to make predictions.

#### Example: Finding the equation

The percent of adults who smoke, recorded every few years since 1967, suggests a negative linear association with no outliers. A line was fit to the data to model the relationship.

**Write a linear equation to describe the given model.**

**Step 1:**Find the slope.

This line goes through left parenthesis, 0, comma, 40, right parenthesis and left parenthesis, 10, comma, 35, right parenthesis, so the slope is start fraction, 35, minus, 40, divided by, 10, minus, 0, end fraction, equals, minus, start fraction, 1, divided by, 2, end fraction.

**Step 2:**Find the y-intercept.

We can see that the line passes through left parenthesis, 0, comma, 40, right parenthesis, so the y-intercept is 40.

**Step 3:**Write the equation in y, equals, m, x, plus, b form.

The equation is y, equals, minus, 0, point, 5, x, plus, 40

**Based on this equation, estimate what percent of adults smoked in 1997.**

To estimate what percent of adults smoked in 1997, we can plug in 30 for x (since x represents years since 1967):

Based on the equation, about 25, percent of adults smoked in 1997.

*Want to practice more problems like these? Check out this exercise.*

## Want to join the conversation?

- How will I know for sure if my rounding to the nearest hundred correct?(5 votes)
- Then you check your answer again and see if you got it right or wrong.(3 votes)

- In the practice it asks for the exact number like if i got a 97 as an average for an answer it says my answer is wrong and the answer is like 95 or 96.(2 votes)
- what if the y intercept is not given how do you find it then(2 votes)
- You can also look at the formula of the equation.(2 votes)

- Does the line have to have a positive slope for there to be a linear relationship?(0 votes)
- Absolutely not! Slopes can be negative too, that just means the slope-intercept formula will look like y=-mx+b instead of y=mx+b(2 votes)

- How would you apply linear regression to a data table?(0 votes)
- You first plot the data points in a scatter plot. If you had "hours playing sports" as your column header, and "mood rating" as your row header, each value could be plotted on a graph, and then you would find the regression line.(1 vote)