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AP Statistics: Chapter 4
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Exponential function
y = abˣ (variable = exponent)
Power function
y = axᵇ (variable = base)
What lists are used for exponential functions?
(L1, L4)
What lists are used for power functions?
(L3, L4)
If a residual plot has a pattern...
A liner regression will not be the best fit
Never round .999...
To 1
To fine which regression fits best...
Find the regression with a correlation coefficient closest to 1 or -1
Extrapolation
The use of a regression line/curve for predictions outside the given domain
Are extrapolated values always correct?
No (sometimes you can get a negative, etc)
When residual is greater than 0...
It was an underestimation
When residual is less than 0...
It was an overestimation
Lurking variables
Have an important effect on the relationship between variables in a study, but are not the variables being studied
Lurking variables can always...
Be identified and explained
Using averaged data...
Smoothes out day to day variations
Individual data...
Shows more scatter about the LSRL and therefore has a lower correlation than averaged data
Correlations based on averaged data...
Are usually too high when applied to individuals
Association
Changes in x values show a change in y values (don't prove)
Causation
Changes in x values cause changes in y values (explains why)
Common response
Both x and y respond to changes in some unobserved variable(s)
Confounding
The effect on y of the explanatory variable x is hopelessly mixed up with the effects on y of the other variable(s)
An observed association _______ always reflect cause and effect
Does not
An association between an explanatory variable x and a response variable y is...
Not by itself good evidence that changes in x actually cause changes in y, even if this association is very strong
Experiment
A methodology to get "good" evidence by changing x and keeping lurking variables under control
With causation you always have...
Association
The added values of the columns and rows should...
Match
Simpson's Paradox
Refers to the reversal of the direction of a comparison or association when data from several groups are combined to form a single group
What does the Simpson's Paradox show?
Breaking data up into groups help show or identify lurking variables that can get hidden when individuals are clumped into one large group
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