Business Forecasting Topic 6

Question 1

Regression Analysis

Answer 1

relationship between variable wanting to predict & other variable = explanation of behaviour

• various aspects of relationship between criterion and 1 or more explanatory variables (effect of explanatory on criterion)
• must distinguish between 2
  -used for forecasting

Question 2

criterion

Answer 2

dependent variable

Question 3

explanatory variable

Answer 3

independent variable

Question 4

correlation

Answer 4

measure strength of association between 2 variables

• initial assessment = scatter diagram
• scatter -> dependent variable = vertical axis (y)

Question 5

regression

Answer 5

describe nature of association between variables

Question 6

regression used to

Answer 6

1. provide understanding of relationship between variables (effectiveness of activities)
2. forecasts made

Question 7

product moment correlation coefficient
PMCC

Answer 7

r
objective measure of strength of association between 2 variables

• 1 = perfect negative correlation
  +1 = perfect positive correlation

Question 8

interpreting correlation

Answer 8

1. high correlation doesn’t imply causal relationship could be due to other factors
2. outliers - distort (outlier or influential) = change correlation
3. small sample -> observed correlation is high but no association
4. PMCC only measures linear

Question 9

2 other causes of a high correlation

Answer 9

1. coincidence (over time period both increase but no link)
2. hidden third variable/lurking variable (influence both variables)

Question 10

Bivariate regression

Answer 10

fitting a line through scatter of points on scatter diagram

Question 11

least squares criterion

Answer 11

best fitting line is one minimising sum of squared vertical direction from line

Question 12

residual or error

Answer 12

vertical deviation from the line

Question 13

best fitting line represented by equation

Answer 13

Question 14

interpolation

Answer 14

explanatory variable in data range = more reliable

Question 15

extrapolation

Answer 15

anything beyond data limits
falls outside of our observed points
- less reliable

• assumption that same linear relationship applies may not be valid

Question 16

coefficient of determination

Answer 16

r squared
measures goodness of fit
values from 0-1.0
1 = perfect fit
e.g. 0.817 = 81.7% of variation is explained

high value doesn’t guarantee obtained the best regression model -> just say model fits past data well (but could yield poor forecasts)

same as co-efficient of correlation

Question 17

significance of the regression line

Answer 17

two variables not related then β is zero

Question 18

population values of intercept and slope

Answer 18

intercept = α
slope = β

Question 19

t - test

Answer 19

null hypothesis
generates a p value
e.g. p = 0.001 -> statistically significant

Question 20

4 assumptions underpinning the significance test

Answer 20

1. sum of errors is 0
2. errors = normally distributed
3. homoscedacity
4. erros associated with any 2 observations are independent

• test how well these are met be inspecting residuals of model

Question 21

homoscedacity

Answer 21

variance of error is same
irrespective of the value of independent variable

Question 22

inspecting the residuals of the regression model

Answer 22

see if assumptions appear to be met - useful to obtain plots of residuals

1. histogram of residuals = reveal cant be normally distributed
2. plotting residuals may reveal assumption of homoscedasticity is not valid
3. plotting residuals against independent -> assumption of linearity is wrong

Question 23

bivariate regression analysis

Answer 23

1. model assumes linear relationship between variables
2. make forecasts = assume relationship observed previously will continue, over time underlying relationship may change
3. only 1 variable used to forecast (others will also be associated)
4. Large residual observation = outlier vs influential observation

Question 24

influential observation

Answer 24

KING KONG EFFECT
- large influence on line of best fit (if omitted from analysis = position of line = change)
- lie to extreme right or left of scatter away from bulk

• draw regression line towards them
• not large residuals therefore not outliers