AP Stats Chapter 3

Explanatory Variable

the variable that explains or affects the outcome (x) or b

Response Variable

the variable that is the outcome (y)

Direction

the direction of the line

• negative or positive 

Form

the shape of the line —> mostly linear but also can be nonlinear(curved or pattern) 

Strength

data that follows the linear pattern + how intact the points are 

Correlation Coefficient r

to quantify the strength of the relationship 

• negative r values: negative correlation 

• positive r values: positive correlation 

Correlation and Causation are not equal, why?

They can strongly correlate, but they are not equal because there could be other factors/variables that could lead the variable down another path—> might not be a causal relationships

LSRL

y^ = a + bx 

Used to determine the line of best fit: sum of squared residuals to get rid of the negatives 

Extrapolation

going beyond the x values listed in the data because the data could change (this is bad)

Residuals

the difference between the actual response value and the predicted value (y^ - y)

Residual Plots

Good Fit—> data is linear if the residuals are scattered and there are no patterns

Bad Fit—> residuals are not scattered and have a sort of pattern 

Point of LSRL

(mean of x values, mean of y values)

Coefficient of Determination

r²

percent of difference in the sum of squared residual errors 

can be used to find r 

Removing low-leverage points (closer to mean of x values)…

do not change the line of best fit that much because the values were closer to x

Removing high-leverage points (farther from mean of x values)…

affect the slope more because they are farther from the mean, affecting it more

If the r² doesn’t match and the pattern is curved (residual plots)…

a log transformation is used to make the values less skewed and more linear

log —> 10^x 

ln—> e^x 

Interpretation of r

There is a direction, strength, and form relationship between x and y values.

Interpretation of r²

We know that r²% of the variation in y can be explained by the linear relationship between x and y.

Interpretation for Se

For a given x, we would expect the y to vary Se above and below the line

Interpretation of the slope (b)

For every 1 unit increase in ________ (x value), our model predicts an increase/decrease of slope in our _________ (y value). 

Interpretation y intercept

When the ____(x value) is 0, our model predicts that the ______ (y value) would be y intercept.