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FORECASTING Regression Analysis Asl? Sencer - PowerPoint PPT Presentation

Graduate Program in Business Information Systems. FORECASTING Regression Analysis Aslı 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

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FORECASTINGRegression AnalysisAslı Sencer

• 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.

Equation:

Slope:

Y-Intercept:

• 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

• 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.

• Variation of actual Y from predicted

• Measured by standard error of estimate, SY,X

• Affects several factors

• Parameter significance

• Prediction accuracy

• 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.

• 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

r = 0

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Coefficient of Correlation and Regression Model

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

• 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

• 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)

Desired Pattern

Error

Error

0

0

Time (Years)

Time (Years)

Pattern of Forecast Error