STAT 211 – 019 Dan Piett West Virginia University Lecture 3

Last Class Measures of Dispersion (Spread) Standard Deviation, IQR Scatterplots Plotting 2 Numeric Variables against each other Correlation r positive, negative, none Regression Using 1 Variable in a scatterplot to predict another y = b1*x+b2

Overview Review of Regression Intro to Probability

Section 3.3 Regression Review

Regression Intro So 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 Regression The 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

Probability Probability is the a measure of the likelihood of an event. Example: Tossing a coin one time P(Heads) = ½ or.5 P(Tails) = ½ or.5 This is called the theoretical probability (p) Now we flip the same coin 100 times. How many heads to we expect?.5*100 = 50 Suppose we actually get 45 heads Our empirical probability ( ) is 45/100 =.45 As your sample gets larger, your empirical probability approaches your theoretical probability

More on Probabilities Probabilities can take on values between 0 and 1 P(A) = 0 Event A will never occur P(A) = 1 Event A will always occur The sum of all probabilities always = 1 Complementary Events P(Not A) = 1- P(A)

Definitions Trial An Action that results in one of several possible outcomes Rolling a die Experiment A single trial or series of trial Rolling one die Sample Space The set of all possible outcomes {1, 2, 3, 4, 5, 6} Event The set of outcomes with something in common Rolling an Even Number A={2, 4, 6}; P(A)=3/6

A Deck Of Cards

An Example A 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 = 16 P(Face Card) = 16/52 Probability of getting a Spade P(Spade) = 13/52 Probability of getting a 2 of Hearts P(2 of Hearts) = 1/52

Compound Events An Event comprised of two (or more) events Example: Rolling a 6 sided die Let Event A be rolling an even number A = {2, 4, 6} Let Event B be rolling a number beginning with “t” B = {2, 3} Union The Set of A or B = {2, 3, 4, 6} Intersection The Set of A and B = {2}

The Addition Rule The Addition Rule can be used to calculate the Union Mutually Exclusive Events Two events that cannot occur simultaneously The Probability of the Intersection is 0 Example: Rolling a Fair Dice Once A = Rolling an Even Number B = Rolling a 5

Conditional Probability Let A be the event that a single die rolls an even number Let B be the event that a single die rolls a 3, 5, or 6 How 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( ) = 1/6 B = {3, 5, 6} P( ) = 3/6