1. 12a. Regression Analysis, Part 1 CSCI N207 Data Analysis Using Spreadsheet Lingma Acheson linglu@iupui.edu Department of Computer and Information Science, IUPUI

2. Student Reading Aptitude Reading Hours 1205 251 352 4357 5308 6358 7103 852 9155 10409 Multivariate Analysis - Correlation Scatter chart with a trend line:

3. 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

4. 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

5. Reviewing the Linear Equation The equation for a line is: Dependent Variable Independent Variable Slope y- intercept

6. Slope and y-intercept Y = 0.4X + 2 Y = 0.8X + 4 Y = 0x + 5

7. m and b m, the Slope is a ratio, defined as: ∆: change of or as

8. Example – Determining Slope Data Points Value X1X1 1 Y1Y1 2.4 X2X2 20 Y2Y2 10

9. 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

10. Practice Find the equation for the line below. p1(5,1), p2(10,3)