Example on the Concept of Regression

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Example on the Concept of Regression
.
observation .
. 1 2 3
4 .
age 25 20 22 30
grade 3 2
4 2

IME 301, Feb. 99
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Use Regression 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
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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, Sept 98
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• Hypothesis Statement about a parameter
• Hypothesis testing decision making
• procedure about the
  hypothesis
• Null hypothesis the main hypothesis H0
• Alternative hypothesis not H0, H1
• Two-sided alternative hypothesis, uses
• One-sided alternative hypothesis, uses gt or lt

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• 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.
• If level of significance is greater than P-value
  then reject H0 .
• Significance level 1 Confidence
  level

IME 301, April 04
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• Common abuses of Regression
• Variables completely unrelated
• not valid for extrapolation!!

IME 301, Sept 98