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Lecture-18-Simple Linear Regression

Lecture-18-Simple Linear Regression - LECTURE 18 Simple...

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LECTURE 18 Simple Linear Regression (Part 2): The Coefficient of Determination This lecture covers material on measuring the goodness of fit for the estimated regression equation using the Coefficient of Determination. Microsoft Excel is used for some applications. Read: Chapter 12, Section 12.3. In Lecture 19, we learnt how to compute the estimated linear regression equation from sample data by using the least squares method. We now want to know how good is the fit between this estimated equation values ( ŷ i ) and the actual observation ( y i ). The measure used for determining the goodness of fit is the Coefficient of Determination. To compute the Coefficient of Determination we need to compute three values: 1. Sum of Squares Due to Error (SSE) 2. Total Sum of Squares (SST) 3. Sum of Squares Due to Regression (SSR) ___________________________________________________________ We will use the example in Lecture 18 shown below to illustrate our computations . A company launches a new product and conducts an extensive advertising campaign for four months with advertising expenditure inceasing every month. It wants to develop an equation showing how sales is related to its expenditure on advertising. The data is shown in the table below. Advertising Expenditure ($ 1000s): 1 2 3 4 Product Sales (in 1000 units): 2 4 4 6 1
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Sum of Squares Due to Error (SSE ) In Lecture 15, we had seen that the Least Squares Method minimizes the sum of the squares of the differences between the observed values of y i and the corresponding estimated values of ŷ i . Therefore the objective of Least Squares method is: Min Σ ( y i - ŷ i ) 2 The difference ( y i - ŷ i ) is also known as the ith residual and represents the error in using ŷ i
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