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# Linear Trend Lines - PowerPoint PPT Presentation

Linear Trend Lines. Y t = b 0 + b 1 X t Where Y t is the dependent variable being forecasted X t is the independent variable being used to explain Y. In Linear Trend Lines, X t is assumed to be t. b 1 is the slope of the line, determined by Excel

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## PowerPoint Slideshow about ' Linear Trend Lines' - komala

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Presentation Transcript

• Yt = b0 + b1 Xt

• Where Yt is the dependent variable being forecasted

• Xt is the independent variable being used to explain Y. In Linear Trend Lines, Xt is assumed to be t.

• b1 is the slope of the line, determined by Excel

• b0 is the y intercept of the line, determined by Excel

Coefficient of Determination: R-square

• Proportion of variation in Y around its mean that is accounted for by the regression model

• 0 <= R2 <= 1

• Will always increase as add more independent variables into regression model. Use adjusted R2 to compare when more than one independent variable is used

• The standard deviation of estimation errors

• The measure of amount of scatter around the regression line

• Can be used as a rough rule of thumb for predicting level of accuracy.

• =trend(known y-range, known x-range, new x)

• Where known y-range are the cells that hold known values for the y variable

• Where known x-range are the cells that hold known values for the x variable

• Where new x is the cell or value for which the y variable is to be forecasted

• Create a trend model and calculate the estimated value for each observation

• Calculate the ratio of the actual value to the predicted value for each observation

• Use the average of the values for each seasonal period to compute the seasonal index

• Multiply any forecast produced by the trend model by the appropriate seasonal index

• Program linear trendline formula for trend forecast, referring to input data cells for b0 and b1

• Program seasonal adjustment formula, referring to input data cells for seasonal indices

• Program MAPE or MSE calculations

• Program Solver to Min MAPE/MSE

By Changing seasonal indices, b0 and b1

Subject to average seasonal index = 100%

and seasonal indices>=0

• Y37 = 185.8 + .372*37 = 199.63

• Seasonal forecast for 37 = seasonal index for 37 * Y37

=1.44* 199.63 = 288.4

• Y38 = 185.8 + .372*38 = 200

• Seasonal forecast for 38 = 1.29*200

= 259

You want to examine the linear dependency of the annual sales of produce stores on their size in square footage. Sample data for seven stores were obtained. Find the equation of the straight line that fits the data best.

Annual Store Square Sales Feet (\$1000)

1 1,726 3,681

2 1,542 3,395

3 2,816 6,653

4 5,555 9,543

5 1,292 3,318

6 2,208 5,563

7 1,313 3,760

Excel Output

From Excel Printout:

Graph of the Sample Regression Line: Example

Yi = 1636.415 +1.487Xi

The slope of 1.487 means that for each increase of one unit in X, we predict the average of Y to increase by an estimated 1.487 units.

The model estimates that for each increase of one square foot in the size of the store, the expected annual sales are predicted to increase by \$1487.