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12a. Regression Analysis, Part 1 CSCI N207 Data Analysis Using Spreadsheet Lingma Acheson linglu@iupui.edu Department of Computer and Information Science, IUPUI
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Student Reading Aptitude Reading Hours 1205 251 352 4357 5308 6358 7103 852 9155 10409 Multivariate Analysis - Correlation Scatter chart with a trend line:
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Multivariate Analysis - Correlation Scatter chart with a trend line: With a trend line, are we able to roughly estimate the reading aptitude if a person reads 6 hours a week? If so, what is the estimation? Student Reading Aptitude Reading Hours 1205 251 352 4357 5308 6358 7103 852 9155 10409 11256 12337.8 134610
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Regression and Prediction Regression refers to a mathematical method for determining the best equation to reproduce a data set. Linear regression is a regression method that applies a straight line (linear model) for analysis. How do we generate a formula that represents a line with which we can use to predict a data without having to use a chart? We use regression analysis to … –… predict new X and Y values –… aid our understanding of data behavior
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Reviewing the Linear Equation The equation for a line is: Dependent Variable Independent Variable Slope y- intercept
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Slope and y-intercept Y = 0.4X + 2 Y = 0.8X + 4 Y = 0x + 5
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m and b m, the Slope is a ratio, defined as: ∆: change of or as
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Example – Determining Slope Data Points Value X1X1 1 Y1Y1 2.4 X2X2 20 Y2Y2 10
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Example of Determining Y-Intercept X 1 =1, Y 1 =2.4, X 2 =20, Y 2 =10, m=0.4 Example 1:Example 2: Equation: Y = 0.4X + 2
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Practice Find the equation for the line below. p1(5,1), p2(10,3)
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