Stats Exam 3

What does r = 1 or -1 tell us?

Strong LINEAR relationship

What does r = 0 tell us?

Strong NONLINEAR relationship or NO LINEAR relationship

correlation

describes the strength & direction of the straight line relationship

What is r?

correlation coefficient

What is line of regression?

(if x on y) a line that makes the squares of the vertical distances of the data points as small as possible

What is possible and what is appropriate?

Possible: compute r and the line of best fit

Appropriate: for linear forms

What is R2?

Coefficient of Determination

What is coefficient of determination?

explains what proportion of the variation in the y variable is explained by regression of y on x

What is R2 between and what does it mean?

0 and 1

• 0 = none of whats going on with y has something to do with whats going on with x

• 1 = y has everything to do with x

ONLY tells us how strong the predictions of y from x will be

Does prediction have to bbe linear?

nope!

What is Extrapolation?

using data outside of the available range

How to tell if data is trustworthy?

if R2 is high / close to 1 and we are NOT extrapolating (it is in the range of data)

Relationship between correlation and causation

causation implies correlation BUT correlation does NOT imply causation

Causation

x causes y

Common Response

x and y both caused by third unmeasured variable

Confounding

difficult to distinguish the effects of x and z on y

What is the gold standard for cause and effect?

experimental study

Evidence for causation?

• strong association

• consistency across multiple studies

• alleged cause precedes effect in time

• plausible explanation for the connection

Myth of Short-Term Regularity

believing sequences should be even

ex. coin flips are INDEPENDENT and do not affect future flips

Myth of Streaks

overrating chance because someone is “on a streak”

ex. Curry’s chances of hitting a free throw — each shot is independent

Myth of Surprising Coincidence

ex. having the same birthday as someone in a room

Personal Probability

personal judgements about the likelihood of certain events ; no mathematical basis

Law of Averages

in a large enough number of trials, the rate at which an event will occur with surely approach the probability

Probability Model

describes all possible outcomes and says how to assign probabilities

Rules of Probabilities

1. between 0 and 1

2. sum of all possible outcomes is 1

3. prob that an event does NOT occur is 1-probability

4. 2 that have no outcomes in common = SUM of individual probabilities

5. if 2 events are independent = probability both will occurs is the PRODUCT

Central Limit Theorem

statistics will be normally distributed (even if underlying distribution isn’t)

Simulation

using random digits from a table/software to imitate chance

• give probability model

• assign digits to outcomes

• do many repetitions