Lecture 9.2 Regression Revision.pptx

# Lecture 9.2 Regression Revision.pptx - 1305AFE Business...

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1305AFE Business Data Analysis Week 10 Simple Linear Regression (Revision) References: Chapter 17 (section 17.1- 17.5)

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objectives To identify the dependent and the independent variables To estimate simple linear regression model parameters Assess the fitness of the linear regression model (R 2 )
Introduction When the problem objective is to analyse the relationship between numerical variables, correlation and regression analysis is the first tool we will study. Regression analysis is used to predict the value of one variable (the dependent variable ) on the basis of other variables (the independent variables ). Dependent variable: denoted Y Independent variables: denoted X

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A model of the relationship between house size (independent variable) and house price (dependent variable) would be: House size House price Most lots sell for \$300 000. Building a house costs about \$800 per square meter. Ho use price = 300 000 + 800(Size) In this model, the price of the house is completely determined by the size. A model…
In real life, however, the house cost will vary even among the same size of house: Same house size, but different price points (e.g. décor options, portico upgrades, lot location…). x House size House price 300K\$ Lower vs. higher variability House price = 300 000 + 800(Size) + A model…

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Random term We now represent the price of a house as a function of its size in this probabilistic model: y = 300 000 + 800x + where (Greek letter epsilon) is the random term (also known as error variable ). It is the difference between the actual selling price and the estimated price based on the size of the house. Its value will vary from house sale to house sale, even if the area of the house (i.e. x ) remains the same due to other factors such as the location, age, décor etc of the house.
Model A straight line model with one independent variable is called a simple linear regression model . It is written as: error variable dependent variable y-intercept slope of the line independe nt variable

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