Stats I Final Pitt 4

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Anonymous
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187307
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Stats I Final Pitt 4
Updated:
2012-12-05 11:49:24
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Regression
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Stats I Final Pitt part 4
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  1. Simple Line Regression

    regression
    performed to test if there is a significant prediction of a DV by an IV (predictor)

    DV is interval/ratio

    uni-directional
  2. Assumptions of Regression

    regression
    Normality of the errors

    No Outliers

    Linearity

    Homoscedasticity

    Independence of subjects
  3. Regression Assumptions: Normality of the errors

    regression
    the distribution of erros is normal

    assumption tested using Shapiro-Wilk
  4. Regression Assumptions: No Outliers

    regression
    no extreme scors among errors.

    assumption tested by examining histograms and Q-Q plots
  5. Regression Assumptions: Linearity

    regression
    the relationship between DV and IV is linear

    • tested by examing scatterplots of:
    • 1. DV vs IV
    • (and/or)
    • 2. errors vs predicted scores

    can be objectively tested using Box Cox transformation
  6. Regression Assumptions: Homoscedasticity

    regression
    variability of DV is same across the levels of an IV

    • tested by examining scatterplots of:
    • 1. DV vs IV
    • and/or
    • 2.errors vs predicted scores

    can be objectively tested using Bruesch-Pagan or White's tests
  7. Regression Assumptions: Independence of Subjects

    regression
    design consideration

    cannot be tested using statistics

    one subject's scores cannot be influenced by another subject
  8. Regression Model

    regression
    • model in statistics that defines a relationship of variable(s) to another variable(s)
    • -how they are related to each other
    • B0 is y-intercept
    • B1 is the regression coefficient (slope)
    • Ei is the error (residual)
  9. Interpretations

    regression
    • b0 is the value of DV predicted, Yhati, when the IV is 0, xi = 0.
    • -Most of the time b0 is not of any interest
    • b1 measures the amount of change in DV predicted, for a single unit increase in IV
  10. Ordinary Least Squares

    regression
    estimates the parameters by minimizing the sum of square errors

    mispredictions should be as small as possible
  11. Errors

    regression
    difference between the DV and predicted DV

    • some are positive while others are negative
    • -below line due to overestimation of scores
    • -above line due to underestimation of scores

    Distance between score and line is the error
  12. Standard Error of the Estimate

    regression
    standard deviation of the errors

    difference between the observed and predicted DV

    "on average, how much each subject is mis-predicted by"
  13. Research question: is there a significant prediction of a DV by an IV?

    regression
    t-test for b1

    df =
    N - 2
  14. Research question: is the y-intercept significantly different than 0?

    regression
    • t-test for b0
    • df = N - 2
  15. Effect Size

    regression
    • measure of effect that is often used in simple linear regression is the coefficient of determination, R2
    • -which measures the proportion of the variability of a DV explained by an IV
    • -ranges from 0 to 1
    • used only for descriptive purposes
    • -descripes sample not population
  16. Adjusted R-square

    regression
    used to make inferences about population

    adjusts for sample size (and the number of IVs)
  17. Beta

    regression
    (spelled out for standardized regression coefficient)

    measures the amount of change in standard unit (i.e. 1 SD) of DV predicted for a one standard unit increase in the DV

    same as r between a DV and IV

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