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2015 AP STATS > UNIT 2 VOCAB AND CONCEPTS > Flashcards

UNIT 2 VOCAB AND CONCEPTS Flashcards

1
Q

What does r tell us?

A

How STRAIGHT a positive or negative relationship is between two QUANTITATIVE variables

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2
Q

What values can r be?

A

from -1 to +1

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3
Q

What are some strong r values and some weak r values

A

Strong r values are close to 1 or -1, like -0.83 or 0.94. Weak r values are close to zero like 0.10 or -0.06

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4
Q

What if a scatterplot goes straight across horizontally?

A

NO ASSOC. That would be like height and IQ. If each height has about the same IQ, then they are INDEPENDENT

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5
Q

If something is correlated is it associated?

A

Yes (if it is straight)

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6
Q

association or correlation?

A

association is talking about a relationship? correlation is an actual calculated number

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7
Q

How to describe association on scatterplot?

A

DIRECTION… FORM.. STRENGTH (and outliers)

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8
Q

direction?

A

positive or negative

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9
Q

form?

A

straight, curved

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10
Q

strength?

A

give the r value (if straight), or say? “tightly packed” or “ loosely packed”

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11
Q

does correlation mean causation?

A

NO WAY DUDE

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12
Q

Give example of incorrectly using the word “correlation”

A

“there is a correlation between gender and video game playing” This person should say “association.” You can’t say correlation because gender is categorical.

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13
Q

does high r value mean anything?

A

An r value alone tells little. CHECK THE SCATTER.. IS IT LINEAR?? make sure it’s linear first.

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14
Q

How is r calculated?

A

r= sum(ZxZy) / (n-1)—- the sum of rectangle areas on standardized axes

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15
Q

how can you check for “straight enough?”

A

residuals plot fool!

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16
Q

how do you interpret slope?

A

for an increas of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]

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17
Q

how do you interpret y intercept?

A

The model predicts that if there were no [x stuff] this is how much [y stuff] you’d have

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18
Q

how to interpret slope EQUATION? rSy/Sx

A

for each increase of 1 st dev in x direction, you go r st dev in y direction.

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19
Q

If r= 0.8.. An x value that is 2 standard deviations above the mean will have a predicted y value that is _______

A

1.6 standard deviations above the mean

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20
Q

if you mult or divide the x’s or y’s (shift/scale) does r change?

A

no. the strength remains the same. (If you log or square it, it will change, but just adding or multiplying won’t change it)

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21
Q

if you switch x and y does r change?

A

NO. The strength stays the same.

22
Q

if you switch x and y will slope change?

A

YES- slope is rsy/sx? to get new slope you do: (r sqared)/old slope

23
Q

Can you predict an X by using a Y?

A

NOT WITH THE SAME EQUATION! BE CAREFUL!! You have to change the entire equation and start from scratch?

24
Q

What point is on every regression line?

A

the mean-mean point. (x bar, y bar)

25
Q

Why is it calle d “least squares regression line?”

A

Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distance to that line (minimizes the squared residuals)

26
Q

interpret r squared

A

r squared % of variability in y can be explained by the model. The rest is in residuals?

27
Q

does high r squared mean a good model?

A

CHECK STRAIGHNESS FIRST. you should check your plot and residuals to make sure model is appropriate and no outliers present? then it means something

28
Q

is r sensitive to outliers?

A

yes. A single outlier can make it seem like there is a relationship (out in x direction..), or that there is none.

29
Q

Look for lurking variables?

A

think hot chocolate sales in caf at wachusett mountain and ski accidents at wachusett mountain. Did the chocolate cause the accident??????

30
Q

outliers in regression?

A

doesn’t follow the “flow” (pinky trick)

31
Q

what about your calculator for using curves to fit curved data?

A

sure.. Quadreg, cubicreg, lnreg, etc? just be careful when substituting while writing the equation given.

32
Q

what does “regression to the mean” mean?

A

preditions for y are closer to the mean y (y bar) than the actual x is to the mean x (in s.d). Sons were closer to average height than the dads. Super tall dads had tall sons, but not super tall sons, on average.

33
Q

what does influential mean?

A

It means that the point, when added or removed to data, will influence the SLOPE.. Generally these are outliers in the x direction?. Far left or right.

34
Q

what is a linear model?

A

it is an equation you can use? or a line of a graph, but it is just a model that says what kind of happens, and can be used to ESTIMATE WHAT MIGHT HAPPEN

35
Q

what is a residual?

A

ACTUAL-PREDICTED. A-P. like this class.. AP (get it?)

36
Q

what is b1 and bo ?

A

b1 is the SLOPE, and bo is the intercept. Remember that bo can be thought of as “b old” it is the old b? the intercept in y=mx+b? so it is still the intercept.

37
Q

what is leverage?

A

leverage just means it is far away from x-bar? far right or left from the middle.. Some leverage points are not influential if they go along with the flow of the scatter.

38
Q

what is the line that you plot?

A

IT IS A MODEL!

39
Q

what is the LSRL

A

the “least squares regression line” that line.. That equation

40
Q

what should we look for in resid plot?

A

curve or pattern.. Also, it should have equalish scatter from left to right

41
Q

what’s up with extrapolation?

A

not a good idea. sometimes it’s all you can do, but still, NOT GOOD

42
Q

which is explanatory variable?

A

x. horizontal axis. it “explains” what happens to y

43
Q

which is response?

A

y.. Vertical axis.. It “responds” to the x

44
Q

will residual plots always show outliers? (will outliers always have large residuals?)

A

Not necessarily.. Some points have so much leverage, they pull the line up to it?

45
Q

What is homoscedasticity?

A

equal scatter along the regression line

46
Q

What if the scatterplot is curved?

A

either straighten it and fit a line, or keep it and fit a curve (quadreg, cubicreg, lnreg, logreg)

47
Q

How can you straighten data?

A

Do stuff to the y (square it, root it, log it, etc) and recheck the plot. Remember to put the transformation into your equation.. Example Sqrt y = 4.33 - 2.03 x

48
Q

How do you undo a log when solving?

A

10^ stuff

49
Q

How do you undo an ln when solving?

A

e^stuff

50
Q

How do you undo sqrt when solving?

A

^2

51
Q

How do you undo squares or cubes?

A

^ 1/2 or ^ 1/3

52
Q

How do you get equation from computer output?

A

y= b0 + b1 x
y is the dependent variable
b0 is the coefficient of constant (or it says intercept)
b1 is the coefficient of the variable given (indep)
x is the indep variable
generally arranged: Y= this down plus this left “

2015 AP STATS (11 decks)

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