Stats I Final Pitt 4

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

DV is interval/ratio

uni-directional

Normality of the errors

No Outliers

Linearity

Homoscedasticity

Independence of subjects

the distribution of erros is normal

assumption tested using Shapiro-Wilk

no extreme scors among errors.

assumption tested by examining histograms and Q-Q plots

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

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

design consideration

cannot be tested using statistics

one subject's scores cannot be influenced by another subject

• 
• 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)
• E_i is the error (residual)

• b₀ is the value of DV predicted, Yhat_i, when the IV is 0, x_i = 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

estimates the parameters by minimizing the sum of square errors

mispredictions should be as small as possible

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

standard deviation of the errors

difference between the observed and predicted DV

"on average, how much each subject is mis-predicted by"

t-test for b₁

df = N - 2

• t-test for b₀
• df = N - 2

• 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

used to make inferences about population

adjusts for sample size (and the number of IVs)

_{(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