1. Trend Projection Model b0b0 b1b1 YiYi << The X variable in a Trend Projection model is the time period t

2. Trend Projection in Excel Two techniques: –On the Chart, select the time series and then right- click to ADD TRENDLINE. Pick the linear trendline option and display the equation and R-square or –On a Worksheet that contains the time series, select the TOOLS menu in Excel 2003 or the DATA tab in Excel 2007; open the DATA ANALYSIS submenu, and select the REGRESSION option in the dialog box. See snippits in Blackboard to add-in the Data Analysis submenu if it does not show up as an option in Excel on your PC at home.

3. Excel’s Regression Option

4. Class Exercise: Trend Projection Output for Trend.xls

5. Trend Projection Model From Excel Printout:

6. The Coefficient of Determination r 2 is a number between 0 and 100% Measures the proportion of variation in Y that is explained by the independent variable X in the regression model In trend projections, you can interpret it as the proportion of variation in Y that is explained by the presence of linear trend.

7. Simple Linear Regression: Example 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

8. Which is the dependent Y variable? A.The Store Number B.The Square Footage of the Store C.The Annual Sales of the Store

9. Which is the independent X variable? A.The Store Number B.The Square Footage of the Store C.The Annual Sales of the Store

10. Scatter Diagram: Example Excel Output

11. Equation for the Sample Regression Line: Example From Excel Printout:

12. Graph of the Sample Regression Line: Example Y i = 1636.415 +1.487X i 

13. Interpretation of Results: Example 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.

14. Restaurant Sales Exercise (Regress.xls) The manager wants to forecast restaurant sales for quarter 11 On the Trend Projection worksheet, generate the Trend Projection output starting in cell A17 and forecast restaurant sales for quarters 1-10 On the Regression worksheet, perform a regression of restaurant sales on student population. Write the regression output starting in cell A17 and forecast restaurant sales for quarters 1-10

15. Trend Projection Output

16. Regression on Student Population Output