Business Forecasting Topic 7

Question 1

multiple regression

Answer 1

• obtain more powerful result if include more than 1 independent (explanatory) variable in model

-> dependent variables explained better

Question 2

model of multiple regression

Answer 2

Question 3

Coefficient of multiple determination

Answer 3

R squared
goodness of fit of model to the data is measured by this

how well explained the variation in dependent variable

Question 4

coefficient of multiple correlation

Answer 4

square root
R

Question 5

changes in R squared

Answer 5

increases/fails to decrease = as no. of independent variables added to regression model increases

even if new independent variables have no relationship with dependent variable (not worth including) -> counteract this with adjusted R squared

Question 6

adjusted r squared equation

Answer 6

big sample = small changes
more variables = adjusted R squared is smaller

corrected for unwanted variables

adjusted for increase in no of independent variables and the sample size

Question 7

significance tests for the multiple regression model

Answer 7

• based on same assumption as bivariate regression model

adress:
1. validity of regression model
2. validity of individual regression coefficient

if I variable = no relationship with D variable = β have a value of zero and true pop relationship would have zeros

Question 8

f-statistic

Answer 8

tests the statistical significance of the whole regression model itself

most computers = give F and associated p-value automatically

e.g. p< 0.0001 = reject H0 model has explanatory power and at least one I variable has non zero coefficient

Question 9

significance of each regression coefficient

Answer 9

each independent = set up hypotheses
t - statistic = test null hypothesis

Question 10

significance testing answers?

Answer 10

1. arisen by chance - model useless for forecasting?
2. goodness of fit
3. variables by chance

Question 11

multicollinearity

Answer 11

• some/all of I variables = highly correlated (related)

2 I highly correlated -> linear combination of a subset of independent variables highly correlated with another

Question 12

f test vs t test

Answer 12

t = individual variables

f = whole regression model

Question 13

problem with multicollinearity

Answer 13

bi’s in the regression model = very imprecise estimates of true regression co-efficients the βi’s -> unreliable
difficult to precisely show the contributions

Question 14

multicollinearity can lead to…

Answer 14

1. estimated coefficients having wrong signs (+ve vs -ve)
2. misleading p values for t-tests -> decision whether to include is wrong

• doenst affect predictive ability of model. danger = misleading indications about relationship natures - to include or not

Question 15

dealing with multicollinearity

Answer 15

• specialised technique
• correlated variables combined in single ‘super variable’ -> principal components analysis

-simplest procedure = 1 or 2 or variables highly correlated - mean model lose predictive power

Question 16

finding multicollinearity

Answer 16

if exists in problem -> look at correlation matrix

if explanatory variable correlated highly with another explanatory = chance of multicollinearity

• or variance inflation factor (VIF) and tolerance (inverse of VIF)
  largest VIF > 10 = multicollinearity

Question 17

Dummy variables

Answer 17

assume values of either 0 or 1

nominal variables - often increase explanatory or predictive power of regression model

multicollinearity among dummy variables = delta by reducing number of dummy variables in equation by 1

Question 18

perfect multicollinearity

Answer 18

impossible to estimate model

Question 19

standardised regression coefficients

Answer 19

• interpretation made easier if coefficients are standardised

standardisation = makes α the constant in regression model disappear - new regression coefficient = beta coefficients

Question 20

beta coefficients

Answer 20

• dont depend on units of measurement of different variables
• give better idea of relative importance of independent variables -> useful to model consumer choice
• tell us relative importance to consumers of different attributes of product

Question 21

building a regression model

Answer 21

• multicollinearity complicate decisions on which variables to include
• prerequisite = adequate theory/rationale to justify decision to include variable
• may be justified to include I variable even if p-value on t test is large

Question 22

automated approaches to model building

Answer 22

1. step wise regression
2. best subsets regression

Question 23

step-wise regression

Answer 23

forward-backward step-wise method
1. identify bivariate model choosing I variable highly correlated with dependent
2. add most predictive power selected and new regression equation
3. both I variables tests to see inclusion is justified

Question 24

limitations of stepwise method

Answer 24

1. potentially useful variable excluded if multicollinearity is present
2. repeated significance tests reduces their power - chose conservative levels when determining inclusion or exclusion (e.g. 1%)

Question 25

best sub sets regression

Answer 25

every model, every combination of I = identified and model with greatest predictive power is selected

Question 26

Forced entry method

Answer 26

Enter in SPSS

all variables considered to making contribution towards outcome (dependent variable) forced into multiple regression = model obtained

initial model of explanatory not significant are removed =final model

Question 27

concerns in using highest adjusted R squared to chose model

Answer 27

-only exceed low threshold to be included - t value only exceeds 1 = model has too many variables
conflicts with principle of parsimony (model as simple as possible)
s

Question 28

concerns with using R squared alone

Answer 28

make us think model is improved through including variables