AP Statistics Chapter 3

Response variable
Measures the outcome of a study, dependent variable, y
Explanatory variable
Attempts to explain observed outcomes, indepdent variable, x
Show the relationship betweeen two quantitive variables (bivariate data). Each individual in a data set appears as a fixed point. All data points are plotted but not connected
Positive association
As x increases, y increases
Negative association
As x increases, y decreases
Correlation (r)
Measures strength and direction ( + or - )
Words to describe strength
Strong (when r is close to 1 or -1), moderately strong/weak, weak (when r is close to 0)
Words to describe direction
Positive, negative
Correlation coefficient
r is resistant or non-resistant to outliers?
If r=1
Perfect positive linear slope
If r=-1
Perfect negative linear slope
What is the units of r?
r has no units
What is the range of r?
-1 < r < 1
Observed value (y) - predicted value (y "hat")
Least squares regression line (LSRL)
The line that makes the sum of the sqaures of the vertical distances of the data points from the line as small as possible. The LSRL minimizes the total area in all of the squares.
AKA "prediction line"
What point is always on the LSRL?
(x¯, y¯ )
Equation of the LSRL
Defining x and y
Where x denotes _______ and y denotes predicted _______
If residual is positive...
residual = (y) - (y "hat")

The predicted y was less than the observed y

Prediction was an underestimate
If residual is negative...
residual = (y) - (y "hat")

The predicted y (y "hat") was greater than the observed y

Prediction was an overestimate
If residual = 0
y - yˆ= 0

y = yˆ

Prediction was accurate
Slope of the LSRL
y-intercept of the LSRL, the predicted y when x=0
Interpretation of the slope of the LSRL
For every one unit increase in ___(x)___ the predicted ___(y)___ increases/decreases on average by ___(b)___ units
Coefficient of determination
Is the proportion of the variation in the values of y that is explained by the LSRL
Coefficient of determination
r² measures...
"how good the LSRL is at predicting y"
Interpretation of coefficient of determination
r² % of the variation in ___(y)___ is accounted for by the LSRL
r² > ?
0 (therefore, always positive)
r is negative or positive?
It can be both
The sign of r matches the sign of...
b1 (slope of the LSRL)
Residual Plot
When asked if a linear model is an appropriate model for the data, you MUST examine the ...
Residual Plot characteristic: Curved patterns
The LSRL will not be the best fit
-Not linear, so a line won't be the best choice
Residual Plot charcteristic: Idealized patterns
Random, uniform scatter of points above and below the LSRL residual
Residual Plot characteristic: Varying spread
As x increases, the prediction will be more accurate for some values and less accurate for others
An observation that lies outside the overall pattern of the other observations.
An observation that if it is removed it would drastically change the result of some calculation (either r or r squared)
R-squared adjusted
When making a graph (including a scatterplot), NEVER forget to LABEL your...
Form, direction, and strength (IN CONTEXT)
"Describing the scatterplot" means to discuss the...