AP Stats Unit 2

How is 2-Variable data usually displayed?

Two-Way/Contingency table

Association

If changes in one variable lead to different distributions between different groups, the two variables are associated

Joint relative frequency

1 cell / entire table

Marginal relative frequency

entire row or column / entire table

Conditional relative frequency

total of 1 cell / its respective row or column

What acronym is appropriate to use when asked to describe scatterplots?

CDOFS:

C- Context

D- Direction

O- Outliers/Unusual features

F- Form 

S- Strength

Correlation coefficient (r)

Quantifies how close data points adhere to a line of best fit / strength of a model

What is the rule about correlation and causation?

Correlation DOES NOT equal causation.

Linear regression equation

ŷ = a+bx

Extrapolation

Using a linear model to predict an x-value outside of the given set

How do you read computer readouts?

a= -87.12

b= 1.5433

x= Constant

y= HEIGHT

Residual

How far a given point is from the model’s prediction

Residual plot

Judges the appropriateness of a model.

How do you know a residual plot is favorable vs not?

You want to see a random distribution with no apparent form.

Least Squares Regression Line (LSRL)

Linear equation that minimizes the sum of squared residuals. (See graphs on 2.8 notes to better understand difference)

Coefficient of determination (r²)

Percent of variation in the response variable that can be explained by the explanatory variable.

What ways can you judge if a linear model is appropriate?

YES: r, Residual scatter plot

NO: r²

Outlier

A point that doesn’t follow the general trend, and therefore impacts the model’s strength because of its large residual

High leverage point

A point with a significantly larger x-value than any other point. CAN follow the general trend, but may impact slope or y-int

If you want to make a graph for categorical subsets of a categorical data, what kinds of plots can you use?
(See 2.1-3 notes for example)

Side by side bar graphs, segmented bar graphs, mosaic plots

Where does the explanatory variable go?

x-axis

Where does the response variable go?

y-axis

What does the slope of a line say about its association

Upward slope- Positive assoc.

Downward slope- Negative assoc.

Can you accurately calculate r for a nonlinear relationship?

No

What does a positive residual indicate?

The model underestimated the response variable.

What does a negative residual indicate?

The model overestimated the response variable.

Is a residual plot appropriate to use if it fans inward/outward?

No

Define an influential point

A point that, if removed, changes the linear regression substantially