STAT 512 Midterm

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Author:
MRK
ID:
293178
Filename:
STAT 512 Midterm
Updated:
2015-01-28 15:41:06
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Simple linear regression
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Notes for the Midterm
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  1. Simple v. Multiple regression
    • Simple: 1 axis
    • Multiple: more than 1
    • Assuming the relationship is linear
  2. Smoothing curve v. Regression line
    • Smoothing curve: Not straight, fits a curve using a given percentage of the points
    • Regression Line: straight line using a statistical method
  3. r2 value (coefficient of multiple determination)
    • how well the model fits
    • how much of the variation is y is explained by x
  4. adjusted r2
    adjusts r2 by dividing each sum of squares by its associated degrees of freedom
  5. residual
    observed-predicted (with the line)
  6. Why do we use simple linear regression?
    • understand cause and effect relationships
    • make decisions on cost
    • to predict outcomes
  7. case or data point
    observed pairs of explanatory x, response y variables
  8. Yi = β0 + β1Xi + εi
    for i (1 to n)
    • Simple linear regression model
    • β0 = intercept
    • β1 = slope
    • ε = independent, normally distributed random errors with mean 0 and variance σ2
  9. ε ~iid N(0,σ2)
    iid = independent
  10. how to find estimates for beta 1 and beta 0
    • from plotting the regression line or
    • Analytical procedure:
    • b1 = Sum(Xi - mean X)(Yi - mean Y) / sum(Xi - mean X)2
    • b0 = mean Y - b1 times mean X
  11. Maximum Likelihood
    A way to find estimators b1 and b0 but they are the same for simple linear regressions
  12. to calc b1 by hand with points
    • b1 = sum(ki times Yi)
    • Ki = (Xi - mean X)/sum(Xi - mean X)2

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