Unit 2 AP States

What are explanatory and response variables?

Explanatory variable: Helps explain or predict (x-axis).

Response variable: Outcome measured (y-axis)

How do you describe a scatterplot?

Direction (Positive/negative)

Form (Linear/curved)

Strength (Strong/moderate/weak)

Outliers (Yes/no)

What does correlation ( r ) measure

Correlation measures the strength and direction of a linear relationship between two variables.

What is the formula for the least squares regression line (lsrl)?

ÿ=a+bx (a = y-intercept, b = slope)

How do you interpret the slope of a regression line?

For additional unit of x, the predicted y changed by b units.

How do you interpret the y-intercept of a regression line?

The predicted value of y when x = 0 (may or may not make sense in context).

What is a residual?

Residual = Actual y - Predicted y

It shows how far off the prediction was.

What does a residual plot tell you?

• Random scatter: Linear model is appropriate.

• Clear pattern: Linear model is not appropriate.

What is the standard deviation of residuals (s)?

The typical size of prediction errors between actual and predicted values.

What does r^2 (coefficient of determination) tell you?

The percent of the variability in the response variable that is explained by the regression on the explanatory variable.

What makes a point “influential”?

If removing the point changes the regression line a lot, it’s influential — especially points far in the x-direction.

When is it inappropriate to use correlation (r)?

• When the relationship is not linear.

• When there are outliers (since r is not resistant).

How do you analyze two categorical variables?

Use a two-way table and calculate:

• Marginal distributions (overall totals)

• Conditional distributions (percent within a group)

What does DUFS stand for when describing a scatterplot?

Direction (positive/negative)

Unusual features (outliers/clusters)

Form (linear/curved)

Strength (strong/moderate/weak)

How do you interpret r^2 (coefficient of determination)?

r^2% of the variability in the response variable is explained by the linear relationship with the explanatory variable.

How to interpret r²

If r^2 = 0.85:

“85% of the variability in AP Exam Scores is explained by the linear relationship with Hours Studied.”

Does correlation imply causation?

No!

A strong correlation does not mean one variable causes the other.

(Association ≠ Causation)

What makes a point an outlier in a scatterplot?

A point that does not follow the overall pattern of the data — either in the y-direction or x-direction.

How is an influential point different from an outlier?

• Outlier: Far from the general trend (mostly in y-direction).

• Influential point: Changes the regression line significantly (often far in the x-direction).

When should you check the residual plot?

After fitting a linear model — to verify if a linear model is appropriate (look for random scatter).

What does a pattern in a residual plot suggest?

A pattern means the relationship may be nonlinear — a straight line is not a good model.

What is extrapolation?

Using a regression model to predict outside the range of the data — risky and unreliable.

What is interpolation?

Using a regression model to predict within the range of the data — generally safer and more reliable.