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Lecture 8

Lecture 8 (week 10)

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Ryerson University
Quantitative Methods
QMS 202
Clare Chua

3/17/2011 Regression Analysis Regression Analysis(RA)is a statistical forecasting model that is concerned with describing and evaluating theip between a given variable (usually called the dependent variable, denoted as Y) and one or more other variable (usually known as thent/exploratory variable, denoted as X) . RA can predict the outcome of a given key business indicator (dependent Simple Linear Regression variablebased on the interactions of other related business drivers (independent /exploratory variables) Analyzes the relationship between two variables, X and Y. The eatonship an bedessced asa uncconofa nearrstaghttne))in equation simple linear regression Chapter 13 Y Y=- +- X lnearegresson lnein o 1 Page 578 -1slope -o X intercept Example 1. For elementary school children, it is possible to predict a students reading ability level by measuring the height Learning Objectives of the student. One X to predict Y Reading_ability = f(height) 1. How to use regression analysis to predict the value of a dependent variable 2. If we assume the value of an automobile decreases by a constant amount each year after its purchase, and for based on an independent variable each mile it is driven, the following linear function would 2. The meanin g of the reg gression predict its value (the dependent variable on the left side coefficients, b and b of the equal sign) as a function of the two independent o variables which are age and miles: 3. To make inferences about the slope and MORE than One X to predict Y Car_value = f(age, miles) correlation coefficient where Car_value, the dependent variable, is the value 4. To estimate mean values and predict of the car, age is the age of the car, and miles is the individual values number of miles that the car has been driven. Dependent Variable (Notation: Y) The variable you wish to predict Example Independent Variable (Notation: X) For elementary school children, it is possible Variable used to make the prediction Simple Linear Regression to predict a students reading ability level A single numerical independent variable X is used to predict the by measuring the height of the student. numerical dependent variable Y In the regression terms, we could say that Multiple Regression Use sevveall independent variables to predict a numerical for elementary school children dependent variable Y. -therre is aa diirecttrellattonnshhip bbettweeeen aa students height and reading ability level One variable X Called the independent or explanatory variable or can be used explain (forecast, predict.) to - a students reading level ability can be a second Y Called the dependent or response variable explained (forecasted) by the students variable height When changes in the variable X leads to predictable change in the variable Y then we say X can be used to explain Y 1 www.notesolution.com3/17/2011 Simple Linear Regression Does this mean that we should conclude Regression analysis allows you to identify the type off that taller children are better readers? relatonnship that exists between a dependent variable NO! (X) and an independent variable (Y) The simplest relationship is the straight line or linear Since for the elementary school children relationship height is usually a good predictor of age Y Y See Figure 13.2 page 579 types of relationshipsferent a ge is a ggood predicp tor of grade level g and finally reading level will be strongly related . to grade level . . . -o . . So while height may allow us to predict reading . . . level for elementary school students we should . . . . not conclude that we should stretch out the Slope=1 . . -o Slope=1 students to make them better readers. x Positive (Direct) Linear RelationNegative (Inverse) Linear Relationship TYPES OF RELATIONSHIPS Recall that when the graph of y versus x tends to be in the straight line, we Regression analysis allows you to identype offeatonsshpip say that there is a linear relationship that exists between a dependent variable (X) and an independent y To predict the straight-line (linear) model variable (Y) . The simplest relationship is the straight line or linear relationship . . . Rule of Thumb concepts . . Slope=1 X Y ,Y XType of
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