W9INSE6220 - 1 INSE 6220 - Week 9 3 Example: The cost of...

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1 INSE 6220 -- Week 9 Advanced Statistical Approaches to Quality Linear Regression Analysis of Variance (ANOVA) Dr. A. Ben Hamza Concordia University 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3 0.046 0.048 0.05 0.052 0.054 0.056 0.058 0.06 0.062 x y 2 Introduction to Regression Analysis Regression analysis is used to: Predict the value of a dependent variable based on the value of at least one independent variable Explain the impact of changes in an independent variable on the dependent variable Dependent variable: the variable we wish to predict or explain Independent variable: the variable used to predict or explain the dependent variable i i 1 0 i ε X β β Y Linear component Population Y intercept Population Slope Coefficient Random Error term Dependent Variable Independent Variable Random Error component 3 Example: The cost of building a new house is about $75 per square foot and most lots sell for about $25,000. Hence the approximate selling price ( y ) would be: y = $25,000 + (75$/ft 2 )( x ) (where x is the size of the house in square feet) House size House Price Most lots sell for $25,000 Building a house costs about $75 per square foot. House Price = 25000 + 75(Size) In this model, the price of the house (dependent variable) is completely determined by the size of the house (independent variable). 4 Example In real life however, the house cost will vary even among the same size of house: House size House Price 25K$ Same square footage, but different price points (e.g. décor options, cabinet upgrades, lot location…) Lower vs. Higher Variability x House Price = 25,000 + 75(Size) +
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Random Error for this X i value Y X Observed Value of Y for X i Predicted Value of Y for X i i i 1 0 i ε X β β Y X i Slope = β 1 Intercept = β 0 ε i Simple Linear Regression Model 6 6 The Simple Linear Regression Model With the simple linear regression model y i = β 0 + β 1 x i + ε i the observed value of the dependent variable y i is composed of a linear function β 0 + β 1 x i of the explanatory variable x i , together with an error term ε i . The error terms ε 1 ,…, ε n are generally taken to be independent observations from a N(0, σ 2 ) distribution, for some error variance σ 2 . This implies that the values y 1 ,…,y n are observations from the independent random variables Y i ~ N ( β 0 + β 1 x i , σ 2 ) 7 Example Car Plant Electricity Usage The manager of a car plant wishes to investigate how the plant’s electricity usage depends upon the plant’s production. The linear model will allow a month’s electrical usage to be estimated as a function of the month’s production. 0 1 Example
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W9INSE6220 - 1 INSE 6220 - Week 9 3 Example: The cost of...

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