TABLE 33. Locating a Regression Line
Year X Y X^2 XY YR
19AA -2 348 4 -696 343.2
19BB -1 377 1 -377 383.4
19CC O 418 O O 423.6
19DD 1 475 1 475 463.8
19EE _2 500 _4 1000 504.0
Total O 2118 10 402- Write the regression equation; extrapolate for the year
in question
Here 7* - 423.6 + 40.2X. For 19JJ: X= 7; YR = 423.6 + 40.2 (7) - 705. Hence, the fore-
cast sales for 19JJ = $705,000. For comparative purposes, the past sales volumes as deter-
mined by the regression line are listed in Table 33.
STANDARD DEVIATION FROM
REGRESSION LINEUsing the data in the previous calculation procedure, appraise the reliability of the regres-
sion line in forecasting future sales by computing the standard deviation of the points in
the scatter diagram, using the regression line as the datum from which the deviation is
measured.
Calculation Procedure:
- Calculate the deviation of each point; square the result
The standard deviation serves as an index of the dispersion of the points in the scatter dia-
gram. The standard deviation cr = V2e^2 /«.
Calculate the value of e for each point, Fig. 36. Enter the results for each year in a tab-
ulation such as Table 34. Then, a = V236.8/5 = 6.9.
TABLE 34, Determining the
Standard Deviation
Year Y- YR = e e^2
19AA 348-343.2= 4.8 23.0
19BB 377-383.4= -6.4 41.0
19CC 418-423.6= -5.6 31.4
19DD 475-463.8= 11.2 125.4
19EE 500-504.0= -4.0 16.0
Total 236.8