OPRE 3360 EXAM 2 || QUESTIONS AND
CORRECT VERIFIED ANSWERS
regression equation - CORRECT ANSWER- equation that describes
the relationship between the expected value of the dependent variable
and the independent variable
regression model - CORRECT ANSWER- the equation that describes
how y is related to x and an error term
Serror, - CORRECT ANSWER- -stdev of error term, σerror
- standard error of the estimate, y-value
-on one of the regression tables that comes up in Excel called "standard
error"
- = to sqrt(MS residual)
MS Residual - CORRECT ANSWER- =SS residual / (n-k-1)
n= # of observations in Excel
k= # of indep variables
prediction interval for an individual Y value at X= Xp - CORRECT
ANSWER- -we only calculate 95% prediction interval
- approximately ŷ -+ (2)(Sε)
- ŷ= β0 + βi X (this value is used as ŷ)
- in house ex: so approximately, w/ 95% confidence, price (dep y var) of
a 2600 (x value) sq ft (ind var) house is between _______ & ________
-can compare the width of the PI to the range of the y-value from the
sample
o if PI narrow compared to range of y-values, it's a good fit (roughly half
is good)
o PI > whole range BAD FIT!
, SS regression - CORRECT ANSWER- = (predicted y - avg y)^2
R^2 - CORRECT ANSWER- SS regression / SS total
-explained squared changes in y / total squared changes in y
-answers question "what percentage of the variation in the sample data
is explained by the model?"
-properties:
o R^2 is always between 0&1
o R^2 = 0 --> model means nothing
o R^2 = 1---> perfect fitting model (almost no residuals)
o Often misused measure: can be manipulated ~judging regression
model on R^2 alone can be misleading
F-test - CORRECT ANSWER- - P-value of F-test is automatically
computed in Excel in Anova table under "Significance F"
o same decision rule: if P-value < α, reject H0
Residual Assumptions - CORRECT ANSWER- 1. errors are normally
distributed w/ mean = 0
2. errs have constant stdev σerror for all X (no heteroskedasticity)
3. errs are not correlated (no autocorrelation)
-plot residuals to see if assumptions are met
o spread of residuals roughly the same for all X values--> no
heteroskedasticity
o residuals do not have obvious trend (increasing, decreasing, cyclic) -->
no auto correlation
how to produce residual plots in Excel - CORRECT ANSWER- Data--
> data analysis --> Regression --> turn on labels --> turn on residual &
residual plots --> make sure X and Y inputs are correct (w/ labels)
now plot residual vs observation #s
highlight residuals--> insert --> scatterplot
sample variance (σ^2) - CORRECT ANSWER- (Xi - sample
mean)^2 / (n-1)
sample proportion (p bar) - CORRECT ANSWER- Xi: 0,1 responses
CORRECT VERIFIED ANSWERS
regression equation - CORRECT ANSWER- equation that describes
the relationship between the expected value of the dependent variable
and the independent variable
regression model - CORRECT ANSWER- the equation that describes
how y is related to x and an error term
Serror, - CORRECT ANSWER- -stdev of error term, σerror
- standard error of the estimate, y-value
-on one of the regression tables that comes up in Excel called "standard
error"
- = to sqrt(MS residual)
MS Residual - CORRECT ANSWER- =SS residual / (n-k-1)
n= # of observations in Excel
k= # of indep variables
prediction interval for an individual Y value at X= Xp - CORRECT
ANSWER- -we only calculate 95% prediction interval
- approximately ŷ -+ (2)(Sε)
- ŷ= β0 + βi X (this value is used as ŷ)
- in house ex: so approximately, w/ 95% confidence, price (dep y var) of
a 2600 (x value) sq ft (ind var) house is between _______ & ________
-can compare the width of the PI to the range of the y-value from the
sample
o if PI narrow compared to range of y-values, it's a good fit (roughly half
is good)
o PI > whole range BAD FIT!
, SS regression - CORRECT ANSWER- = (predicted y - avg y)^2
R^2 - CORRECT ANSWER- SS regression / SS total
-explained squared changes in y / total squared changes in y
-answers question "what percentage of the variation in the sample data
is explained by the model?"
-properties:
o R^2 is always between 0&1
o R^2 = 0 --> model means nothing
o R^2 = 1---> perfect fitting model (almost no residuals)
o Often misused measure: can be manipulated ~judging regression
model on R^2 alone can be misleading
F-test - CORRECT ANSWER- - P-value of F-test is automatically
computed in Excel in Anova table under "Significance F"
o same decision rule: if P-value < α, reject H0
Residual Assumptions - CORRECT ANSWER- 1. errors are normally
distributed w/ mean = 0
2. errs have constant stdev σerror for all X (no heteroskedasticity)
3. errs are not correlated (no autocorrelation)
-plot residuals to see if assumptions are met
o spread of residuals roughly the same for all X values--> no
heteroskedasticity
o residuals do not have obvious trend (increasing, decreasing, cyclic) -->
no auto correlation
how to produce residual plots in Excel - CORRECT ANSWER- Data--
> data analysis --> Regression --> turn on labels --> turn on residual &
residual plots --> make sure X and Y inputs are correct (w/ labels)
now plot residual vs observation #s
highlight residuals--> insert --> scatterplot
sample variance (σ^2) - CORRECT ANSWER- (Xi - sample
mean)^2 / (n-1)
sample proportion (p bar) - CORRECT ANSWER- Xi: 0,1 responses
