PSYC 333 Lecture Notes - Lecture 12: Null Hypothesis, Total Variation, Direct Comparison Test
7 May 2018
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PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
Lecture 12
Simple & Multiple Linear Regression
Linear Regression: Assumptions
Linear regression assumes that
Values of Y are independent and are sampled at random from the
population.
The relationship between X and Y is linear (linearity).
Y is distributed normally at each value of X (normality).
The variance of Y at every value of X is the same (homogeneity of
variances)
there should be linear association between X & y from beginning
normality: all values of Y = normally distributed at each level of x variable
Linearity assumption
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PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
“Statistics for Managers”4th Edition, Prentice-Hall 2004
Normality assumption
Homogeneity of variance assumption
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find more resources at oneclass.com
PSYC 305 – STATISTICS FOR EXPER DESIGN, WINTER 2018
Checking assumptions: Residual Analysis
Graphical Analysis of Residuals – “Residual plot”
Difference between Yi & Y
̂i
• Plot residuals vs. Xi values
• Standardized residuals are often used (residuals
divided by their standard errors)
Purposes
Examine functional form (Linear vs. Nonlinear)
Evaluate violations of assumptions
we plot all y values against x values
standardized residuals
Residual plot
for functional form
if you have any particular pattern of data points, means all 3 assumptions are satisfied
at the same time.
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Document Summary
Values of y are independent and are sampled at random from the population. The relationship between x and y is linear (linearity). Y is distributed normally at each value of x (normality). Difference between yi & y i: plot residuals vs. xi values, standardized residuals are often used (residuals divided by their standard errors) Evaluate violations of assumptions we plot all y values against x values standardized residuals. Residual plot for functional form if you have any particular pattern of data points, means all 3 assumptions are satisfied at the same time. Residual plot for equal variances cone shaped = unequal variances equal variance assumption is violated. Residual plot for independence linear pattern of data points means independence assumption is violated. Linear multiple regression simple linear regression then we have more than one independent variable at the same time: multiple regression.
