MGSC 291 - EXAM 2 QUESTIONS WITH ANSWERS.

MGSC 291 - EXAM 2 QUESTIONS WITH |\ |\ |\ |\ |\ |\ |\




ANSWERS

covariates
x - vector of inputs
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bike ex: sunny, 65 degrees, etc
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independent variable that affects the coefficient |\ |\ |\ |\ |\




coefficients (including the intercept) |\ |\ |\




β is your vector
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constant variable affected by covariate
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f( )
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is some link function
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linear regression 𝑓(𝑥 ′𝛽) |\ |\ |\




= 𝑥 ′𝛽|\ |\

,models a CONTINUOUS NUMERIC response
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logistic regression, 𝑓(𝑥 ′𝛽)|\ |\ |\




= 𝑒^ 𝑥′𝛽 / (1 + 𝑒^ 𝑥′𝛽)
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models a BINARY response (y is either 0/1 or T/F)
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E[Y|x]
linear regression |\




expected value (average/conditional mean) value of Y given x
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SLR (simple linear regression)
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only 1 input of (x)
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= 𝛽0 + 𝛽1x1
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P(Y=1|x)
logistic regression |\

, probability that Y is equal to 1 given x |\ |\ |\ |\ |\ |\ |\ |\




(y=1 is the outcome of interest)
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linear regression assumption
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𝑦 = 𝑥 ′𝛽 + 𝜀, 𝜀~𝑁(0, 𝜎 2 )
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variability around the linear line is normally distributed with
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constant residual error variance |\ |\ |\




𝜎 2 (variance): is the common variance of errors/residuals, so we
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assume the points are just as spread out no matter where on the
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line


sample data is representative of population
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observations are independent of one another |\ |\ |\ |\ |\




linear relationship between response and covariae(s)
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𝜀
independent errors (variations in y that are NOT correlated with
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x)




log-log model formula |\ |\