#### Transcript of Linear Regression Part 2 - AP Stats Chapter 8

**Linear Regression**

AP Stats - Chapter 8 Part 2

**Assumptions and Conditions**

1. Tthe Quantitative Variable Condition

It makes no sense to create a scatterplot for categorical data, so make sure you have quantitative data.

2. The Straight Enough Condition

Check your scatter plot and decide if it is straight enough for a LINEAR regression.

3. The Outlier Condition

Check for outliers. If there are outliers, then find the regression with and without the outlier.

**Residual Plots**

How do I make a residual plot?

What am I hoping to find with a residual plot?

The answer to that question is . . .

**NOTHING!**

Nothing? What do you mean, "NOTHING"?

You want your residual plot to be very boring.

When a residual plot shows no pattern or direction, or when it doesn't have any interesting features . . .

. . . it means that the original scatterplot is "straight enough".

**For example . . .**

This residual plot shows no pattern or curve, so the straight enough condition is satisfied.

But this residual plot shows an oscilating pattern and tells us that the original scatterplot is probably not linear.

This residual plot shows a definate pattern and doesn't satisfy the "straight enough" condition.

What is the difference between r and r-squared?

Remember . . .

r is the correlation coefficient and . . .

r-squared in called the . . .

Coefficient of Determination

But what's the difference?

Watch and learn my young Padawan . . .

Is there anything else I need to know?

Just a little bit more. We're almost finished with this maze.

Extrapolation

**Here are a few more things to be aware of . . .**

Don't fit a straight line to a NON-LINEAR relationship.

Always check the scatterplot, r, and the residual plot for straightness.

Beware of extraordinary points.

If you have one point that is far from the others, find the regression with and without the point.

Don't extrapolate beyond the given data.

Don't infer that x causes y just because you've got a good linear model.

Don't choose a model based on r-squared alone.

One last thing . . .

Just kidding! See you in stats class . . .

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