STAT 211 – 019Dan Piett

West Virginia University

Lecture 3

Last ClassMeasures of Dispersion (Spread)

Standard Deviation, IQRScatterplots

Plotting 2 Numeric Variables against each otherCorrelation

rpositive, negative, none

RegressionUsing 1 Variable in a scatterplot to predict

anothery = b1*x+b2

OverviewReview of RegressionIntro to Probability

Section 3.3

Regression Review

Regression IntroSo we have decided that two variables are

correlated, we are now going to use the value of one of the variables, “x”, to predict the value of the other variable, “y”.

Example:Use height (x) to predict weight (y)Use temperature (x) to predict ice cream

sales (y)

Regression Equation

Calculating a Regression Equation Given the slope and intercept

Plotting a Regression Line

Notes on Regression Lines

Residuals

New Info on RegressionThe sign of the slope of the regression

equation will always match the sign of the correlation coefficient

The regression line minimizes the squared residuals

Section 4.1

Intro to Probability

ProbabilityProbability is the a measure of the likelihood of an

event.Example: Tossing a coin one time

P(Heads) = ½ or .5P(Tails) = ½ or .5This is called the theoretical probability (p)

Now we flip the same coin 100 times. How many heads to we expect?.5*100 = 50Suppose we actually get 45 headsOur empirical probability ( ) is 45/100 = .45

As your sample gets larger, your empirical probability approaches your theoretical probability

More on ProbabilitiesProbabilities can take on values between 0

and 1P(A) = 0

Event A will never occurP(A) = 1

Event A will always occurThe sum of all probabilities always = 1Complementary Events

P(Not A) = 1- P(A)

DefinitionsTrial

An Action that results in one of several possible outcomes

Rolling a dieExperiment

A single trial or series of trialRolling one die

Sample SpaceThe set of all possible outcomes{1, 2, 3, 4, 5, 6}

EventThe set of outcomes with something in commonRolling an Even Number A={2, 4, 6}; P(A)=3/6

A Deck Of Cards

An ExampleA Deck of Playing Cards (52 cards, 4 suits,

13 number/faces)Probability of getting a face card, counting

Aces?4 Jacks, 4 Queens, 4 Kings, 4 Aces = 16P(Face Card) = 16/52

Probability of getting a SpadeP(Spade) = 13/52

Probability of getting a 2 of HeartsP(2 of Hearts) = 1/52

Compound EventsAn Event comprised of two (or more) eventsExample: Rolling a 6 sided die

Let Event A be rolling an even numberA = {2, 4, 6}

Let Event B be rolling a number beginning with “t”B = {2, 3}

UnionThe Set of A or B = {2, 3, 4, 6}

IntersectionThe Set of A and B

= {2}

The Addition RuleThe Addition Rule can be used to calculate

the Union

Mutually Exclusive EventsTwo events that cannot occur simultaneouslyThe Probability of the Intersection is 0

Example: Rolling a Fair Dice OnceA = Rolling an Even NumberB = Rolling a 5

Conditional ProbabilityLet A be the event that a single die rolls an

even numberLet B be the event that a single die rolls a 3, 5,

or 6How about the probability of an event, given

another event?What is the P(A|B)?

P(A|B)= P( )/P(B) = 1/3 = {6}

P( ) = 1/6B = {3, 5, 6}

P( ) = 3/6