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AP Statistics: Chapter 3
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Gravity
Terms in this set (51)
Response variable
Measures the outcome of a study, dependent variable, y
Explanatory variable
Attempts to explain observed outcomes, indepdent variable, x
Scatterplots
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
When the variables aren't dependent, the first part of the data is...
Independent, x
All points on a scatterplot must be...
Labeled
CAR words
Correlation, association, and relationship
Positive association
As x increases, y increases
Negative association
As x increases, y decreases
Clustered data is "almost"...
Bimodal
Correlation
Measures strength and direction
Words to describe strength
Strong (r>.99), moderately strong/weak, weak
Words to descrie direction
Positive, negative
Correlation coefficient
r
r is resistant or non-resistant?
Non-resistant
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
Regression line
A line that describes how a response variable (y) changes as the explanatory variable (x) changes
Error
Observed value - predicted value
Least squares regression line (LSRL)
The LSRL of y on x is 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.
What point is always on the LSRL?
(x¯, y¯ )
Equation of the LSRL
yˆ = a + bx
LSRL cookie cutter #1
Where x denotes _______ and y denotes predicted _______
If error is positive...
The prediction was less and the observed was more
b
Slope
LSRL cookie cutter #2
For every one unit increase in ___(x)___ the predicted ___(y)___ increases/decreases on average by ___(b)___ units
Sum of sqaures about the mean y¯ (SSM)
Sum of squares for error
Coefficient of determination
Is the fraction of the variation in the values of y that is explained by the LSRL
r²
Coefficient of determination
r² equation
(SSM-SSE)/SSM
r² measures...
Variability along LSRL
SSE measures...
Variability above and below the LSRL
As the SSE decreases, |r|and r²...
Gets closer to 1, and linearity for the data is stronger
Strength and direction are indicated by ___ but actually measured by ___
r, r²
Interpretation of coefficient of determination cookie cutter #2
r² % of the variation in ___(y)___ is accounted for by changes in ___(x)___
r² > ?
0
r is negative or positive?
It can be both
The sign of r matches the sign of...
b
Residuals
The difference between an observed value of the respponse variable and the value predicted by LSRL
Residual equation
y - yˆ
If residual >0
-y - yˆ> 0
-y > yˆ
-Observed > predicted
-Prediction was an underestimate
If residual <0
-y - yˆ< 0
-y < yˆ
-Observed < predicted
-Prediction was an overestimate
If residual = 0
-y - yˆ= 0
-y = yˆ
-Observed < predicted
-Prediction was accurate
Residual Plot charcteristic: Idealized patterns
Show uniform scatter of points above and below the LSRL residual
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 characteristic: Varying spread
As x increases, the prediction will be more accurate for some values and less accurate for others
Outlier in the y direction
-Large residual
-Not influential
Outlier in the x direction
-Influential because including this point will drastically change the slope of the LSRL
-It will change the slope of the line
R-squared adjusted
NEVER USE
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