FORECASTING Regression Analysis Aslı Sencer

1 / 17

# FORECASTING Regression Analysis Aslı 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' FORECASTING Regression Analysis Aslı Sencer' - lamis

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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.
Linear Regression Equations

Equation:

Slope:

Y-Intercept:

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

r = -1

Y

Y

^

Y

=

a

+

b

X

i

i

^

Y

=

a

+

b

X

i

i

X

X

r = .89

r = 0

Y

Y

^

^

Y

=

a

+

b

X

Y

=

a

+

b

X

X

X

i

i

i

i

Coefficient of Correlation and Regression Model
Coefficient 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)

Trend Not Fully Accounted for

Desired Pattern

Error

Error

0

0

Time (Years)

Time (Years)

Pattern of Forecast Error