Example on the Concept of Regression . observation

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Presentation transcript:

Example on the Concept of Regression . observation . . 1 2 3 4 . . 1 2 3 4 . age 25 20 22 30 grade 3 2 4 2 Example on the Concept of Two-Factor Analysis . observation . . 1 2 3 4 . age 25 20 22 30 grade 3 2 4 2 year 4 2 3 3 IME 301, Feb. 99

Use Regression or Two-Factor Analysis to check if: We can conclude any relation between factors. (one or two factors on another factor) We can judge on reliability of our conclusion. IME 301, Feb. 99

ei = residual = Yi - Regression Analysis Y = + X + Y = dependent variable, response variable X = independent variable, regressor, predictor = error regression coefficients: = intercept = slope Yi = observed Y at point Xi = predicted Y at point Xi , = + Xi ei = residual = Yi - Method of Least Square: minimize sum of ei2 IME 301

Hypothesis testing on slope: H0 : = 0 (That is there is no relationship between X and Y) H1 : 0 (That is there is some relationship between X and Y) Find t statistics and P-value from Excel output for discussion. Then fail to reject H0 if OR IME 301

Common abuses of Regression: Variables completely unrelated Not valid for extrapolation IME 301