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## Digital SAT Math

### Course: Digital SAT Math > Unit 3

Lesson 6: Scatterplots: foundations# Scatterplots | Lesson

A guide to scatterplots on the digital SAT

## What are scatterplots?

A

**scatterplot**displays data about two variables as a set of points in the x, y-plane. Each axis of the plane usually represents a variable in a real-world scenario. In this lesson, we'll learn to:

- Use the line of best fit to describe scatterplots
- Make predictions using the line of best fit
- Fit functions to scatterplots

This lesson builds upon the following skills:

- Data representations
- Graphs of linear equations and functions
- Quadratic graphs
- Exponential graphs

**You can learn anything. Let's do this!**

## How do we talk about scatterplots?

### Bivariate relationship linearity, strength and direction

## What is the line of best fit?

### Interpreting a trend line

### The line of best fit

While each point in a scatterplot represents a

*specific observation*, the**line of best fit**describes the*general trend*based on all of the points.For a given data point, we expect to see a difference between its y-value and the y-value predicted by the line of best fit. These differences are used for more advanced statistical analysis; for the SAT, we only need to calculate the difference.

We can also interpret the slope and y-intercept of the line of best fit the same way we interpret line graphs:

- The slope represents a constant rate of change.
- The y-intercept represents an initial value.

### Try it!

## How do I use the line of best fit to make predictions?

### Line of best fit: smoking in 1945

### Predicting what we can and cannot see

When making predictions based on scatterplots,

*always*use the line of best fit instead of individual data points.If the prediction lies within the part of the x, y-plane shown, it must lie on the line of best fit.

If the prediction lies beyond the part of the x, y-plane shown, we can either extend the line of best fit or use its equation to find the prediction.

### Try it!

## How do I fit functions to scatterplots?

### Use direction and intercepts to determine the best fit

On the SAT, questions that ask you to fit a function to a scatterplot are always multiple choice, and all four choices are usually functions of the same type, e.g., four linear functions or four quadratic functions.

For linear functions in the form f, left parenthesis, x, right parenthesis, equals, m, x, plus, b:

- Sketch a line that fits the data and approximate its slope.
- The value of m should match the slope. Make sure to pay attention to the signs!
- Approximate the y-intercept of the function that best fits the data. Make sure the constant term b matches the y-intercept.

For quadratic functions in the form f, left parenthesis, x, right parenthesis, equals, a, x, squared, plus, b, x, plus, c:

- Sketch a parabola and approximately fits the data.
- If the parabola opens upward, a should be positive. If the parabola opens downward, a should be negative.
- Approximate the y-intercept of the function that best fits the data. Make sure the constant term c matches the y-intercept.

### Try it!

## Your turn!

## Want to join the conversation?

- Great explanation! Thank you!(17 votes)
- I just want to draw straight lines like Sal does.(15 votes)
- Tell me if I’m wrong, but it can be broken down to two things on the SAT: a frown face is -ax^2 and a smile is ax^2 (I’m referring to the shape of the curve - frown 🙁negative and smile 🙂positive) and the y intercept is -c if below x axis and c if above.(8 votes)
- Yeah, you understood it right!(1 vote)

- I felt the Last 3,4 examples were quite hard! And KA doesn't add an explanation to these:( Please add the explanation to these ASAP!(6 votes)
- How can we formulate quadratic equations out of graphs? I don't think there has been a lesson regarding this till now(4 votes)
- We won't have to. We will have to choose between the options given to us, to find the quadratic equation most suitable to the scatterplot(3 votes)

- The beard question in the quiz section almost killed me of laughter hahahahha(5 votes)
- Guessing the line between the dots=frustrating(4 votes)
- "For a given data point, we expect to see a difference between its y-value and the y-value predicted by the line of best fit. These differences are used for more advanced statistical analysis; for the SAT, we only need to calculate the difference." I didn't understand this at all, could someone please expalin me? How do I calculate this difference?(2 votes)
- When we make equations and lines of best fit, they are models and approximations of general trends in the graph. Of course, individual actually measured data points won't all be on this line, because all we're doing is making a prediction/approximation. Each data point then can be above or below the line's prediction for that x-value by a certain amount. If we reduce the differences, then our line of best fit will probably be better (that's where the r and r^2 that you might have seen if you've ever done linear regression come from).

On the SAT, the max that we'll have to do is calculate the difference between the predicted y-value and the actual data point y-value. This difference just means subtracting one from the other, that's all. A common theme for an SAT problem might be to give you the equation of the line of best fit and a data point, and ask you to calculate the difference. Here, you would have to plug in the x-value to your equation to find the predicted y, then subtract that from the actual y to see by how much it differs. Hope this helps!(4 votes)

- I did not understand at all. I always guess. 😭😭(3 votes)
- Doesn’t The one question in the practice section has the slop of 5/2?(2 votes)