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Graduate Program in Business Information Systems

FORECASTINGRegression AnalysisAslı Sencer

Regression in Causal Models

- Regression analysis can make forecasts with with a non-time independent variable.
- A simple regression employs a straight line.

Ŷ(X) = a + bX

- The dependent variable is not time periods, such as:
- store size
- order amount
- weight
- For 10 rail shipments, the transportation time Y was forecast for specific distance X.

Interpretation of Coefficients

- Slope (b)
- Estimated Y changes by b for each 1 unit increase in X
- If b = 2, then transportation time (Y) is expected to increase by 2 for each 1 unit increase in distance (X)
- Y-intercept (a)
- Average value of Y when X = 0
- If a = 4, then transportation time (Y) is expected to be 4 when the distance (X) is 0

Least Squares Assumptions

- Relationship is assumed to be linear.
- Relationship is assumed to hold only within or slightly outside data range.
- Do not attempt to predict time periods far beyond the range of the data base.

Random Error Variation

- Variation of actual Y from predicted
- Measured by standard error of estimate, SY,X
- Affects several factors
- Parameter significance
- Prediction accuracy

Assumptions on Error Terms

- The mean of errors for each x is zero.
- Standard deviation of error terms , SY,X
- is the same for each x.
- Errors are independent of each other.
- Errors are normally distributed with mean=0 and
- variance= SY,X. for each x.

Correlation

- Answers: ‘how strongis the linearrelationship between the variables?’
- Correlation coefficient, r
- Values range from -1 to +1
- Measures degree of association
- Used mainly for understanding

r = -1

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r = .89

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Coefficient of Correlation and Regression ModelCoefficient of Determination

If we do not use any regression model, total sum of square of errors, SST

If we use a regression model, sum of squares of errors

Then sum of squares of errors due to regression

We define coef. of determination

Coefficient of determination r2 is the variation in y

- that is explained and hence recovered/eliminated
- by the regression equation !
- Correlation coeficient r can also be found by using

Multiple Regression in Forecasting

- Regression fits data employing a multiple regression equation with several predictors:

Ŷ = a + b1X1 + b2X2

- Floorspace X1 and advertising expense X2 make forecasts of hardware outlet sales Y:

Ŷ = -22,979 + 11.42X1 + 23.41X2

- The above was obtained in a computer run using 10 data points.
- Forecast with X1 =2,500 sq.ft. and X2=$750:

Ŷ = -22,979+11.42(2,500)+23.41(750)=$23,129

Guidelines for Selecting Forecasting Model

- You want to achieve:
- No pattern or direction in forecast error
- Error = (Yi - Yi) = (Actual - Forecast)
- Seen in plots of errors over time
- Smallest forecast error
- Mean square error (MSE)
- Mean absolute deviation (MAD)

Desired Pattern

Error

Error

0

0

Time (Years)

Time (Years)

Pattern of Forecast Error

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