Stat Test 4

interpreting r²

____ of the variation in the ___ values can be explained by the line of regression

log-log

log y hat = a + b(logx)

MINI TAB finding r

r = sq root of r²

interpret scatter plot

strong positive linear relationship, negative, moderate, no relation

residual plot linearity

a pattern creates a problem with the linearity (curved residuals/outliers), you want random residuals above and below 0 line

extrapolation

never predict y-values higher than your highest data point or lower than your lowest data point

write line of regression

(predicted # of ____) = a + b(# of ___)

or y hat = a + bx, where y hat = predicted # of ___ and x = # of ___

slope

every time the # of x goes up by 1, the predicted # of y goes up by b(slope), on average

y - intercept

when the # of x is 0 the predicted # of y is a(y-intercept), on average

MAGIC: r²

r² is the proportion of variation in the y-values explained by the line of regression

finding a residual plot

y- y hat

Interpreting Se

Se is the average y - distance your points are away from the line of regression

Finding Se

Se = sq root of ssresid/n-2 (Find ss resid through sum(L3²)

transformations

transform data until linear than run linear regression (logs, log L1 and L2 into columns L3 and L4 then find linear regression)

MINITAB OUTPUT y intercept

constant, coefficient

MINI TAB slope

____, coefficient

MINI TAB r²

r-sq

MINI TAB Se

S

chance experiment definition

situation in which there is uncertainty about outcome

chance experiment examples

rolling a six sided die once, picking one card from a deck

Sample Space

set of all possible outcomes of a chance experiment

mutually exclusive/disjoing

two events are mutually exclusive or disjoint if they both can not happen at the same time

classical probability

if every outcome in the sample space of a chance experiment is equally likely then the probability of E or P(E) is P(E) = the # of outcomes including #/total # of outcomes in sample space (Works as long as outcome is equally likely)

Law of Large Numbers

As the # of repetitions of a chance experiment increases its relative frequency approaches the true probaility. If the # of trials is very large then: P(E)=The # of times E occurs/The total # of trials

probability rule

probability is always between 0 and 1

The NOT Rule

P(Not E) = 1 - P(E)

The OR Rule

P(E or F) = P(E) + P(F) - P (E And F)

If E and F are mutually exclusive in the OR rule..

P(E or F) = P(E) + P(F)

The AND rule

basis of sampling, P(A and B) = P(A) x P(B/A)

P(B/A)

The probability that B occurs GIVEN THAT A occurs: conditional probability (only way to string successive trials in a chance experiment, Ex: roll die twice