Lecture8 - ECO 220Y Lecture 8 Numerical Descriptive...

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ECO 220Y Lecture 8 i l D i t i T h i P t 4 Numerical Descriptive Technique Part4 Migiwa Tanaka Reading: 4.4 (pp.129-137), 4.7, 4.8 1
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Outline umerical Measures Describing Linear Relationship Numerical Measures Describing Linear Relationship between two variables ovariance (Lecture 7) Covariance (Lecture 7) Coefficient of Correlation (Lecture 7) Coefficient of Determination (See textbook & HW) Least Square Method Ordinary Least Square Method Definition Interpretation 2
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What is your qualitative and quantitative assessment of relationships between x and y1, y2, y3 and y4? 10 20 5 -5 0 -20 -10 0 5 x1 -5 0 5 x2 15 51 3 -5 0 5 x2 -5 0 5 10 x3
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Least Square Method If there are two points, there is a How about the case like unique line connecting the line. below? 16 4 14 12 y 10 8 4 20 30 40 50 60 70 80 90 100 x 20 30 40 50 60 70 80 90 100 x
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Least Squares Method -Continued he least square method is a way to fit a line in scatter The least square method is a way to fit a line in scatter plots. l f l i i di t Formula for a line in x-y coordinates: y= a + b x Our task is to find values of a : b: he idea is to find a line that minimizes the sum of The idea is to find a line that minimizes the sum of squared distance from all points.
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