Lecture21

# Lecture21 - STAT 350 Lecture 21 Chapter 3 Bivariate and...

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STAT 350 Lecture 21 Chapter 3 Bivariate and Multivariate Data and Distributions

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Topics Scatter Plots Correlation Fitting a Line to Bivariate Data
Bivariate Data Example First thing we need is some sort of plot…

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3.1 Scatterplots 40 45 50 55 60 65 70 155 160 165 170 175 180
Scatter plot Plots bi-variate data Plot the ( x,y ) pairs directly on plot Pattern within plot can indicate certain relationships between x and y Linear Quadratic, Cubic? Nonlinear? Exponential or Log?

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3.2 Pearson’s Correlation Coefficient The Pearson’s correlation coefficient measures the strength and direction of the linear relationship Examples: Father’s height and son’s height Age and Bone Density Weight and Blood Pressure
Karl Pearson (1857 1936) Sir Francis Galton (1822 1911) Thinking about the degree to which children resemble their parents Kar Pearson (Student of Galton) Conducted a study on the resemblances of family members Measured the height of 1078 fathers and their sons at maturity Scatter plot helps to see the relationship between father’s height and son’s height

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How to calculate Correlation Where: See Example 3.3 in text on page 108.
Properties of Correlation Coefficient Always takes values between -1 and 1 Sign indicates type of relationship Positive As X increases, Y also increases Negative As X increases, Y decreases (and vice versa) Value indicates strength If r is near 0, it implies a weak (or no) linear relationship Closer to +1 or -1 suggests very strong linear pattern If switch roles of X and Y r doesn’t change Unit free unaffected by linear transformations

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Examples Would the correlation between the age of a used car and its price be positive or negative? Why? ( antiques are not included ) What about the correlation between weight of a vehicle and miles per gallon?
Example (ex 14 on page 114) An employee of an auction house has a list of 25 recently sold paintings. Eight artists were represented in these sales. The sale price of each painting is on the

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## This note was uploaded on 04/23/2011 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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Lecture21 - STAT 350 Lecture 21 Chapter 3 Bivariate and...

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