# Stats I Final Pitt 4

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 Author: Anonymous ID: 187307 Filename: Stats I Final Pitt 4 Updated: 2012-12-05 11:49:24 Tags: Regression Folders: Description: Stats I Final Pitt part 4 Show Answers:

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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

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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