Multiple Regression - Reading 5

Question 1

How to interpret the intercept coefficient?

Answer 1

if the dividend
payout Ratio is 0 and the slope of the yield curve is 0, we would expect the subsequent 10 year real earnings growth sale to be
- 11,67.

Question 2

How to interpret the slope coefficient?

Answer 2

If the payout ratio increases by 1%, we would expect the dependent variable to increase by b, holding everything else constant

Question 3

How to formulate a hypothesis for statistical significance?

Answer 3

h0:b=0
Ha:b<>0

Question 4

how to calculate the t-statistic for statistical significance?

Answer 4

t=(^b-0)/Sd(^b)

Question 5

how many degrees of freedom to use for statistical significance??

Answer 5

df=n-k-1

Question 6

What is the p-value

Answer 6

The p-value is the smallest value of significance for which the null hypothesis can be rejected

Question 7

What 8 important informations are you able to calculate with an ANOVA table?

Answer 7

• Coefficient of determination
• F statistic
• standard error of estimate
• SST
• RSS
• SSE
• MSE
• MSR

Question 8

Why do we need to calculate a adjusted coefficient of determination

Answer 8

Unfortunately , R2 by itself may not be a reliable measure of the explanatory power of the multiple regression.
This is because the coefficient of determination almost always increase as variables an added to the model even if the marginal contribution of the new variables isn’t statistically significant. Consequently, a relative
high R may reflect the impact of a large set of independent variables rather than how well the set explains the
dependent variable
*will always be less or equal R^2

Question 9

How to calculate an adjusted coefficient of determination?

Answer 9

Adj. R^2={[(n-1)/(n-k-1)]x[1-R^2]}

Question 10

How to interpret the coefficient of dummy variables?

Answer 10

Th estimated regression coefficient for dummy variables Indicates the difference in the dependent variable for the category represented by the dummy variable and the average value of the dependent variable for all classes
except the dummy variable o class
n -1 variables

Question 11

What is heteroskedasticity? and What are the types and with one is the major problem?

Answer 11

heteroskedasticity occurs when the variane of the residuals is not the same across all observations in the sample
CONDITIONAL—> MAJOR PROBLEM
UNCONDITIONAL

Question 12

What is heteroskedasticity effect?

Answer 12

• sd unreliable
• coefficients aren’t affected
• t-statistics unreliable
• F-statistics unreliable

Question 13

How to detect heteroskedasticity?How to calculate the test statistic?

Answer 13

Scatter plot or Breusch-Pagan
BP Statistic= n x R^2_resid
*one-tailed test

Question 14

How to correct heteroskedasticity?

Answer 14

robust sd (white corrected)

Question 15

What is serial correlation?

Answer 15

because of a tendancy of the data to cluster together from observation to observation, positive serial correlation typically
results in coefficient standard error that are too small, even though the estimated efficient are consislant. To many Type I error!!!

Question 16

How to spot serial correlation?

Answer 16

reisdual Plot or DW statistic

if n too large: DW=2(1-r)

Question 17

How to detect serial correlation?

Answer 17

DW for n large: DW= 2(1-r)
h0: No positive serial correlation

DW=2 -> error terms homocadastic and
not serially correlated (r=0)
DW<2 -> error terms are positively
serially correlated (r ›o)
DW>2 -> error terms are negatively
serially correlated (r<0)

Decision rule:
0——————d1——————-d2—————-
Reject Ho / Inconclusive / Do not reject H0

Question 18

How to correct serial correlation?

Answer 18

• Hanssen Method -> Corrects for serial correlation and heteroskedasticity
• but if serial correlation is not sa problem it is best to use the White corrected sd instead
• Improve the specification

Question 19

What is multicollinearity?

Answer 19

the condition when two or more at the independent variables, or linear combinations of the independent variables, in a multiple regression are highly correlated with each other. This condition distorts the standard error of estimate and the coefficient standard arsons, leading to problems when conducting t-test for statistical significance of parameters

Question 20

What is multicollinearity effect?

Answer 20

• coefficientts are consistent but unreliable
• SD errors inflated
• incorrectly conclude that a variable is not stat. significant -> Type II error

Question 21

How to detect multicollinearity?

Answer 21

• none of the individual coefficient is significantly different from zero
• F-test is statistically significant
• Coefficient of determination is high

Question 22

How to correct multicollinearity?

Answer 22

omit one or more of the correlated variables