AP Statistics Chapter 3

Measures an outcome of a study (dependent variable in a way)

Helps to explain or predict changes in a response variable (independent)

Plot that shows the relationship between two quantitative variables measured on the same individuals.

Direction: Association (Positive/Negative)
Form: Approximately Linear or Curved
Strength: Weak, Medium, Strong
Unusual Features: Outliers

Describe the Association IN CONTEXT

Example: Students who took longer to run 40 yards had shorter jump lengths (Association in context). The relationship between the two quantitative variables reveals a positive association while having a linear form, a strong strength. There is one unusual feature at the 25 yard mark, which deviates slightly from the overall pattern.

The direction and strength of a linear relationship between two quantitative variables. Correlation is always between -1 and 1.

If r>0, the association is positive.
If r<0, the association is negative.
If r=0, the association is none.
This is how you quantify it.

Mention the direction and strength!

EX: The R-value of _____ indicates the linear relationship between the number of points scored versus the amount of turnovers is strong and positive.

It does not imply what caused something!
Correlation measures strength and direction.
Correlation is not a resistant measure (one point can have a drastic change)
Correlation makes NO distinction of the explanatory and response variable.
Correlation is not affected by data transformations.

A line that describes how a response variable (y) changes as an explanatory variable (x) changes. Often used to predict the value of y for a given value of x.

^
y = a +bx

The use of a regression line for prediction far outside the interval of values of the explanatory variable used to obtain the line. These predictions ARE NOT ACCURATE

The prediction error from a regression line. It is the difference between an observed value compared to the predict value.

EQUATION: Residual = Observation-Prediction

A line that makes the sum of the squared residuals as small as possible.

A point in an LSRL that has a substantially larger or smaller x-value than the other observations have.

EX: Low X value, high Y value.

A point in an LSRL that is any point that, if removed, changes the relationship substantially.

The approximate size of a typical prediction error (residual)

You state what the residual is (show how you got it), then say if it is above or below the predicted outcome of the response variable.

EX: The residual for the point (8,2) is -14.47, showing that given 8 seconds of tapping time, the result for the amount of soda left (in mL) is 14.47 BELOW the predicted outcome.

LSRL.

If we don’t square the deviations, they will add up to 0.

They intersect at the LSRL.

A scatterplot of the residuals against the explanatory variable. Residual plots help determine whether a linear model is appropriate.

A linear plot can be chosen if there is no pattern.

The fraction of the variation in the values of y that is accounted for by the LSRL of y on x. FORMAT:

______% of the variation in [response variable] is accounted for by the linear (exponential/power) model relating [response variable] to [explanatory variable].

Correlation and Regression

^
ln(y) = a+b*ln(x)

^
ln(y) = a+b*x

^
y = e^a+b*log(x)

^
y = e^a+b*x

Square the correlation!

______% of the variation in [response variable] is accounted for by the linear (exponential/power) model relating [response variable] to [explanatory variable].