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BUS310_L21_4.5.11

# BUS310_L21_4.5.11 - Inferential Statistics Simple...

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Lecture 21: Inferential Statistics / Simple Regression Chapter 12 (12.1,2,3,5)
1. When do you use Regression Analysis? Regression analysis enables you to develop a model: To predict the value of a numerical (dependent) variable based on the value of at least one numerical (independent) variable E.g., predict monthly sales based on advertisement expenditures (1 independent variable – Chapter 12) E.g., predict monthly sales based on advertisement expenditures, price, shelf space (3 independent variables – Chapter 13)) To explain the impact of changes in an independent variable on the dependent variable, based on the mathematical relationship (regression equation) Dependent variable: the variable we wish to predict or explain

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Regression-based models are used for many types of business analyses: Examples: Advertising and Marketing Effect of an advertisement on sales , based on a set of factors Data mining / predict patterns of consumer behavior Finance Market timing model – predicts return of stocks in the next 3 to 5 years, based on dividend yield of the stock market and interest rate of 90-day treasury bills Publishing Effects of price changes on sales Real Estate Zillow.com develops estimates on the market values of homes based on their features and locations
Simple Linear Regression Simple Linear Regression Model: - Only one independent variable , X - Movie box office success (in \$ millions) - Always one dependent variable , Y - Number of DVDs sold (in thousands) - Causal relationship: Changes in Y (DVD’s sold) are assumed to be caused by changes in X (box office revenue) - Relationship between X and Y is described by a 55

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Correlation vs. Regression Correlation analysis is used to measure strength of the association (linear relationship) between two variables Correlation is only concerned with strength of the relationship No causal effect is implied with correlation Regression implies causal relationship (Changes in Y are assumed to be caused by changes in X) A scatter diagram can be used to show the relationship between two variables
Simple Linear Regression Chapter 12.1, 12.2 1. How to use regression analysis to predict the value of a dependent variable based on an independent variable 2. The meaning of the regression coefficients b0 and b1 3. Use regression to predict individual values Chapter 12.3, 12.5 1. How do you evaluate the strength of the relationship ? 2. What assumptions need to be checked when you use regression? 3. How do you check the assumptions? What to do when they are violated? Next Lecture: 1. Use regression to make inferences about the slope and correlation coefficient 2. Use regression to estimate mean values

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Overview: Simple Regression Sections 12.1, 12.2 1. How do you visualize if a linear relationship exists?
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