RejectwhenShape
MCRasamp
modelmis
specifications
Eth
statistitted restricted
Reading 1: Key Concepts
SCHWESERNOTES - BOOK 1 B Pagan heterostudasticity
TEEEmigration
onlyomissionofvers biased inconsistentwefts
LOS 1.a
Multiple regression models can be used to identify relationships between variables, to forecast variables, or to test existing theories.
LOS 1.b
The general multiple linear regression model is:
Yi = b0 + b1X1i + b2X2i + … + bkXki + εi
The intercept term b0 is the value of the dependent variable Y when all the independent variables (X) are equal to zero. The slope
coe!cient bi is the estimated change in the dependent variable for a 1-unit change in variable i, holding all other independent variables
constant.
LOS 1.c
minimise E
Assumptions underlying a multiple regression model include:
A linear relationship exists between the dependent and independent variables.
The residuals are normally distributed.
The variance of the error terms is constant for all observations.
The residual for one observation is not correlated with that of another observation.
95 ofobsbetween 1.65stddev
The independent variables are not random, and there is no exact linear relation between any two or more independent variables.
LOS 1.d
An ANOVA table is used to assess the usefulness of a regression model's independent variable(s) in explaining the dependent variable:
df SS
Source MS Meanhomosaedasticity
Square = (SS/df)
(Degrees of Freedom) (Sum of Squares) noserial
correlation
nomulticollinearity
Regression k RSS MSR
Error n–k–1 SSE MSE
Total n–1 SST
SSE RSS RSS
MSE = ; MSR = ; R2 =
n–k-1 k SST
Akaike's information criterion (AIC) and Schwarz's Bayesian information criteria (BIC) are used to evaluate competing models with the
same dependent variable. AIC is used if the goal is a better forecast, while BIC is used if the goal is a better goodness of fit.
SSE
AIC =n×ln ( ) + 2(k + 1)
n
varing
SSE
BIC =n×ln (
n ) + ln(n)×(k + 1)
where:
k = the number of independent variables
yÉeg as.rs 1 In ii 11 r
LOS 1.e affectedby t stat
goodnessoffit
NOTmodelfit statsigofvars
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Page 1 of 3
, g is
Fsgint statisticsrestricted
Reading 1: Key Concepts
SCHWESERNOTES - BOOK 1
siglevelFeetif pvalueislower
Unreliableresidsonlyaffectstd errs hypothesistests
vanaffectbothestimates stderrs
MEASUREOFERROR
LOS 1.a
Multiple regression models can be used to identify relationships between variables, to forecast variables, or to test existing theories.
MSE forecast
LOS 1.b
LOWER better
The general multiple linear regression model is: goodnessof fit
Yi = b0 + b1X1i + b2X2i + … + bkXki + εi miseriffy
The intercept term b0 is the value of the dependent variable Y when all the independent variables (X) are equal to zero. The slope
coe!cient bi is the estimated change in the dependent variable for a 1-unit change in variable i, holding all other independent variables
constant.
LOS 1.c
Assumptions underlying a multiple regression model include:
A linear relationship exists between the dependent and independent variables.
The residuals are normally distributed. SSEonly
The variance of the error terms is constant for all observations.
The residual for one observation is not correlated with that of another observation.
The independent variables are not random, and there is no exact linear relation between any two or more independent variables.
LOS 1.d
An ANOVA table is used to assess the usefulness of a regression model's independent variable(s) in explaining the dependent variable:
r o ss a.nl
df SS
onetailedwhentestingif
Source
(Degrees of Freedom) (Sum of Squares)
MS Mean Square = (SS/df) al 0
Regression k RSS MSR
Error n–k–1 SSE MSE
economic
Total stellar n–1 SST
PIET Ya efficient sagacity te
SSE RSS RSS ACChaveneter
shedaticity
MSE = ; MSR = ; R2 =
n–k-1 k SST
Akaike's information criterion (AIC) and Schwarz's Bayesian information criteria (BIC) are used to evaluate competing models with the
ifcorrwithan
same dependent variable. AIC is used if the goal is a better forecast, while BIC is used if the goal is a better goodness of fit.
SSE
AIC =n×ln ( ) + 2(k + 1)
n
landathighlycorrI
SSE
BIC =n×ln (
n ) + ln(n)×(k + 1)
where:
k = the number of independent variables shallnetiedto
LOS 1.e
shouldberelative notabsolute
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Page 1 of 3
MCRasamp
modelmis
specifications
Eth
statistitted restricted
Reading 1: Key Concepts
SCHWESERNOTES - BOOK 1 B Pagan heterostudasticity
TEEEmigration
onlyomissionofvers biased inconsistentwefts
LOS 1.a
Multiple regression models can be used to identify relationships between variables, to forecast variables, or to test existing theories.
LOS 1.b
The general multiple linear regression model is:
Yi = b0 + b1X1i + b2X2i + … + bkXki + εi
The intercept term b0 is the value of the dependent variable Y when all the independent variables (X) are equal to zero. The slope
coe!cient bi is the estimated change in the dependent variable for a 1-unit change in variable i, holding all other independent variables
constant.
LOS 1.c
minimise E
Assumptions underlying a multiple regression model include:
A linear relationship exists between the dependent and independent variables.
The residuals are normally distributed.
The variance of the error terms is constant for all observations.
The residual for one observation is not correlated with that of another observation.
95 ofobsbetween 1.65stddev
The independent variables are not random, and there is no exact linear relation between any two or more independent variables.
LOS 1.d
An ANOVA table is used to assess the usefulness of a regression model's independent variable(s) in explaining the dependent variable:
df SS
Source MS Meanhomosaedasticity
Square = (SS/df)
(Degrees of Freedom) (Sum of Squares) noserial
correlation
nomulticollinearity
Regression k RSS MSR
Error n–k–1 SSE MSE
Total n–1 SST
SSE RSS RSS
MSE = ; MSR = ; R2 =
n–k-1 k SST
Akaike's information criterion (AIC) and Schwarz's Bayesian information criteria (BIC) are used to evaluate competing models with the
same dependent variable. AIC is used if the goal is a better forecast, while BIC is used if the goal is a better goodness of fit.
SSE
AIC =n×ln ( ) + 2(k + 1)
n
varing
SSE
BIC =n×ln (
n ) + ln(n)×(k + 1)
where:
k = the number of independent variables
yÉeg as.rs 1 In ii 11 r
LOS 1.e affectedby t stat
goodnessoffit
NOTmodelfit statsigofvars
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Page 1 of 3
, g is
Fsgint statisticsrestricted
Reading 1: Key Concepts
SCHWESERNOTES - BOOK 1
siglevelFeetif pvalueislower
Unreliableresidsonlyaffectstd errs hypothesistests
vanaffectbothestimates stderrs
MEASUREOFERROR
LOS 1.a
Multiple regression models can be used to identify relationships between variables, to forecast variables, or to test existing theories.
MSE forecast
LOS 1.b
LOWER better
The general multiple linear regression model is: goodnessof fit
Yi = b0 + b1X1i + b2X2i + … + bkXki + εi miseriffy
The intercept term b0 is the value of the dependent variable Y when all the independent variables (X) are equal to zero. The slope
coe!cient bi is the estimated change in the dependent variable for a 1-unit change in variable i, holding all other independent variables
constant.
LOS 1.c
Assumptions underlying a multiple regression model include:
A linear relationship exists between the dependent and independent variables.
The residuals are normally distributed. SSEonly
The variance of the error terms is constant for all observations.
The residual for one observation is not correlated with that of another observation.
The independent variables are not random, and there is no exact linear relation between any two or more independent variables.
LOS 1.d
An ANOVA table is used to assess the usefulness of a regression model's independent variable(s) in explaining the dependent variable:
r o ss a.nl
df SS
onetailedwhentestingif
Source
(Degrees of Freedom) (Sum of Squares)
MS Mean Square = (SS/df) al 0
Regression k RSS MSR
Error n–k–1 SSE MSE
economic
Total stellar n–1 SST
PIET Ya efficient sagacity te
SSE RSS RSS ACChaveneter
shedaticity
MSE = ; MSR = ; R2 =
n–k-1 k SST
Akaike's information criterion (AIC) and Schwarz's Bayesian information criteria (BIC) are used to evaluate competing models with the
ifcorrwithan
same dependent variable. AIC is used if the goal is a better forecast, while BIC is used if the goal is a better goodness of fit.
SSE
AIC =n×ln ( ) + 2(k + 1)
n
landathighlycorrI
SSE
BIC =n×ln (
n ) + ln(n)×(k + 1)
where:
k = the number of independent variables shallnetiedto
LOS 1.e
shouldberelative notabsolute
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Page 1 of 3
