MGSC 291 - EXAM 2 QUESTIONS WITH |\ |\ |\ |\ |\ |\ |\
ANSWERS
covariates
x - vector of inputs
|\ |\ |\ |\
bike ex: sunny, 65 degrees, etc
|\ |\ |\ |\ |\
independent variable that affects the coefficient |\ |\ |\ |\ |\
coefficients (including the intercept) |\ |\ |\
β is your vector
|\ |\ |\
constant variable affected by covariate
|\ |\ |\ |\
f( )
|\
is some link function
|\ |\ |\
linear regression 𝑓(𝑥 ′𝛽) |\ |\ |\
= 𝑥 ′𝛽|\ |\
,models a CONTINUOUS NUMERIC response
|\ |\ |\ |\
logistic regression, 𝑓(𝑥 ′𝛽)|\ |\ |\
= 𝑒^ 𝑥′𝛽 / (1 + 𝑒^ 𝑥′𝛽)
|\ |\ |\ |\ |\ |\ |\
models a BINARY response (y is either 0/1 or T/F)
|\ |\ |\ |\ |\ |\ |\ |\ |\
E[Y|x]
linear regression |\
expected value (average/conditional mean) value of Y given x
|\ |\ |\ |\ |\ |\ |\ |\
SLR (simple linear regression)
|\ |\ |\
only 1 input of (x)
|\ |\ |\ |\
= 𝛽0 + 𝛽1x1
|\ |\ |\
P(Y=1|x)
logistic regression |\
, probability that Y is equal to 1 given x |\ |\ |\ |\ |\ |\ |\ |\
(y=1 is the outcome of interest)
|\ |\ |\ |\ |\
linear regression assumption
|\ |\
𝑦 = 𝑥 ′𝛽 + 𝜀, 𝜀~𝑁(0, 𝜎 2 )
|\ |\ |\ |\ |\ |\ |\ |\ |\
variability around the linear line is normally distributed with
|\ |\ |\ |\ |\ |\ |\ |\ |\
constant residual error variance |\ |\ |\
𝜎 2 (variance): is the common variance of errors/residuals, so we
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
assume the points are just as spread out no matter where on the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
line
sample data is representative of population
|\ |\ |\ |\ |\
observations are independent of one another |\ |\ |\ |\ |\
linear relationship between response and covariae(s)
|\ |\ |\ |\ |\
𝜀
independent errors (variations in y that are NOT correlated with
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
x)
log-log model formula |\ |\
ANSWERS
covariates
x - vector of inputs
|\ |\ |\ |\
bike ex: sunny, 65 degrees, etc
|\ |\ |\ |\ |\
independent variable that affects the coefficient |\ |\ |\ |\ |\
coefficients (including the intercept) |\ |\ |\
β is your vector
|\ |\ |\
constant variable affected by covariate
|\ |\ |\ |\
f( )
|\
is some link function
|\ |\ |\
linear regression 𝑓(𝑥 ′𝛽) |\ |\ |\
= 𝑥 ′𝛽|\ |\
,models a CONTINUOUS NUMERIC response
|\ |\ |\ |\
logistic regression, 𝑓(𝑥 ′𝛽)|\ |\ |\
= 𝑒^ 𝑥′𝛽 / (1 + 𝑒^ 𝑥′𝛽)
|\ |\ |\ |\ |\ |\ |\
models a BINARY response (y is either 0/1 or T/F)
|\ |\ |\ |\ |\ |\ |\ |\ |\
E[Y|x]
linear regression |\
expected value (average/conditional mean) value of Y given x
|\ |\ |\ |\ |\ |\ |\ |\
SLR (simple linear regression)
|\ |\ |\
only 1 input of (x)
|\ |\ |\ |\
= 𝛽0 + 𝛽1x1
|\ |\ |\
P(Y=1|x)
logistic regression |\
, probability that Y is equal to 1 given x |\ |\ |\ |\ |\ |\ |\ |\
(y=1 is the outcome of interest)
|\ |\ |\ |\ |\
linear regression assumption
|\ |\
𝑦 = 𝑥 ′𝛽 + 𝜀, 𝜀~𝑁(0, 𝜎 2 )
|\ |\ |\ |\ |\ |\ |\ |\ |\
variability around the linear line is normally distributed with
|\ |\ |\ |\ |\ |\ |\ |\ |\
constant residual error variance |\ |\ |\
𝜎 2 (variance): is the common variance of errors/residuals, so we
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
assume the points are just as spread out no matter where on the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
line
sample data is representative of population
|\ |\ |\ |\ |\
observations are independent of one another |\ |\ |\ |\ |\
linear relationship between response and covariae(s)
|\ |\ |\ |\ |\
𝜀
independent errors (variations in y that are NOT correlated with
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
x)
log-log model formula |\ |\
