BUAL 2650 EXAM 3 - AUBURN
UNI.QUESTIONS & ANSWERS!!
when setting up null hypothesis - ANSWERslope is usually set equal to zero
use the standard error of the regression slope to estimate - ANSWERthe standard
deviation of the regression slope
three things that affect variability of the slope: - ANSWER1. Spread around the line
(se) - want to be linear and close
2. Spread of x values (sx) - don't want the data clustered
3. sample size (n) - want a large sample size
degrees of freedom for confidence interval - ANSWERn-2
regression equation - ANSWERintercept coefficient + independent variable
coefficient(x)
SE(b1) aka standard error of regression slope - ANSWERis standard error of
independent variable
what does the intercept in the regression equation tell you - ANSWERwhat y hat
would equal if x=0
the slope tells you - ANSWERwith an increase in x you get ____ amount times x
increase/decrease
b1 is an estimate of change in y for a one unit change in x
assumptions and conditions - ANSWER1. linearity assumption
2. independence assumption
3. equal variance assumption
4. normal population assumption
check in that order
linearity assumption - ANSWERThis condition is satisfied if the scatterplot of x and y
looks straight when viewing a scatterplot. A scatterplot of the residuals against x
should have no pattern
Independence Assumption - ANSWERlook for randomization, check plot for lack of
patter or clumping
equal variance assumption - ANSWERthe variability of y should be about the same
for all values of x
, Regression coefficients are interpreted as the amount by which their categories differ
from the baseline - ANSWERafter allowing for the linear effects of the other variables
in the model.
indicator variables - ANSWEREach location has a different intercept, but they all
have the same slope
an interaction exists - ANSWERbetween two independent variables if the
relationship between the mean value of the dependent variable and one of the
independent variables depends upon the value (or level) of the other independent
variable.
interactions - ANSWERhave different slopes and different intercepts
for interactions - ANSWERWe combine our independent variable with our indicator
variable. (multiply)
normal population assumption - ANSWERAssume the errors around the idealized
regression line at each value of x follow a Normal model.
no pattern
if p value is small and we reject - ANSWERWe have evidence that the slope of the
regression line differs from 0 and can conclude that there is a linear relationship
HA for multiple regression - ANSWERAT LEAST ONE does not equal 0
check p value to determine - ANSWERif F is significant or not
if we reject Ho - ANSWERrelationship is significant
p value - ANSWERis significance f column
R squared - ANSWERtells us what proportion of variance is accounted for in the y-
variable by knowing the x-variable
varies from 0-1
the closer to 0 R squared is - ANSWERthe smaller the relationship between x and y
If R Squared = 1 - ANSWERthen the x-variable perfectly explains all the variation in
the y-variable.
Data from scientific experiments often have R2 - ANSWER80%-90% range
Data from observational studies may have an acceptable R2 - ANSWERin the 30%-
50% range
In general, R2 - ANSWERalways increases as more independent variables are
added to the model.
UNI.QUESTIONS & ANSWERS!!
when setting up null hypothesis - ANSWERslope is usually set equal to zero
use the standard error of the regression slope to estimate - ANSWERthe standard
deviation of the regression slope
three things that affect variability of the slope: - ANSWER1. Spread around the line
(se) - want to be linear and close
2. Spread of x values (sx) - don't want the data clustered
3. sample size (n) - want a large sample size
degrees of freedom for confidence interval - ANSWERn-2
regression equation - ANSWERintercept coefficient + independent variable
coefficient(x)
SE(b1) aka standard error of regression slope - ANSWERis standard error of
independent variable
what does the intercept in the regression equation tell you - ANSWERwhat y hat
would equal if x=0
the slope tells you - ANSWERwith an increase in x you get ____ amount times x
increase/decrease
b1 is an estimate of change in y for a one unit change in x
assumptions and conditions - ANSWER1. linearity assumption
2. independence assumption
3. equal variance assumption
4. normal population assumption
check in that order
linearity assumption - ANSWERThis condition is satisfied if the scatterplot of x and y
looks straight when viewing a scatterplot. A scatterplot of the residuals against x
should have no pattern
Independence Assumption - ANSWERlook for randomization, check plot for lack of
patter or clumping
equal variance assumption - ANSWERthe variability of y should be about the same
for all values of x
, Regression coefficients are interpreted as the amount by which their categories differ
from the baseline - ANSWERafter allowing for the linear effects of the other variables
in the model.
indicator variables - ANSWEREach location has a different intercept, but they all
have the same slope
an interaction exists - ANSWERbetween two independent variables if the
relationship between the mean value of the dependent variable and one of the
independent variables depends upon the value (or level) of the other independent
variable.
interactions - ANSWERhave different slopes and different intercepts
for interactions - ANSWERWe combine our independent variable with our indicator
variable. (multiply)
normal population assumption - ANSWERAssume the errors around the idealized
regression line at each value of x follow a Normal model.
no pattern
if p value is small and we reject - ANSWERWe have evidence that the slope of the
regression line differs from 0 and can conclude that there is a linear relationship
HA for multiple regression - ANSWERAT LEAST ONE does not equal 0
check p value to determine - ANSWERif F is significant or not
if we reject Ho - ANSWERrelationship is significant
p value - ANSWERis significance f column
R squared - ANSWERtells us what proportion of variance is accounted for in the y-
variable by knowing the x-variable
varies from 0-1
the closer to 0 R squared is - ANSWERthe smaller the relationship between x and y
If R Squared = 1 - ANSWERthen the x-variable perfectly explains all the variation in
the y-variable.
Data from scientific experiments often have R2 - ANSWER80%-90% range
Data from observational studies may have an acceptable R2 - ANSWERin the 30%-
50% range
In general, R2 - ANSWERalways increases as more independent variables are
added to the model.
