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Unformatted text preview: Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 10 Week 10 topics l Simple linear regression l Method of least squares l Basic assumptions of regression model l Inference & explanatory power l Key references l Keller Chapter 16 and 13.1 22 Recall (end of) week 2 lectures l Introduced problem of fitting a line of best fit to a bivariate scatter of points l Example used was Keller ex.2.88 l Hours of Internet use modelled as a function of Education 33 20 25 30 Simple regression l Have ( Y i, X i) pairs for i = 1, … , n l Obtain line of best fit by minimizing residual sum of squares (ordinary least squares) l Produces estimates of intercept & slope in the linear regression relationship Y i = β 0 + β 1 X i + ε i l Sign of slope coefficient is same sign as covariance (& correlation) between Y i & X i 44 55 Simple regression… 66 Numerical versus statistical properties l Ordinary least squares (OLS) can be viewed as curve fitting l Provides a description of multivariate data l But we also want to make inferences about parameters of the population regression function l How can we use b 1 to make inferences about β 1? l What are the properties of b 1 as an estimator of β 1? l Will also want to use regression models to make predictions or forecasts l If a company increases advertising expenditure what is the predicted impact on sales? l What is the confidence interval for that prediction? 77 Some basics l Terminology l Y i is the dependent variable l X i is the independent or explanatory variable l ε i is the disturbance or error term l β 0 & β 1 parameters to be estimated Some basics… l Population regression relationship is Y i = β 0 + β 1 X i + ε i l Links the (X,Y) pairs via the unknown parameters and the unobserved errors l OLS produces Y i = b 0 + b 1 X i + ei l The predicted regression relationship links the (X,Y) pairs via estimated parameters and calculated residuals 88 99 Some basics… l Disturbance term ε i plays a crucial role in regression l Distinguishes regression models from deterministic functions l Represents factors other than X i that affect Y i l Regression treats these other factors as unobserved l β 1 is the marginal effect of X i on Y i holding these other factors constant l Reliable estimates of β 1 will require assumptions restricting the relationship between...
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