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Unit 9: Regression Analysis

12. The fitted trend is termed as the best in the sense that the sum of squares of deviations of Notes
observations, from it, are minimized.
13. The procedure for calculation of the two constants is highly different for even and odd
number of observations.
14. The general form of linear trend equation is Y = a + bt.
t
15. The mathematical form of a parabolic trend is given by Yt = a + bt - ct or Y = a + bt – ct 2
2
16. The general form of an exponential trend is Y = a.bt
17. Given the mathematical form of the trend to be fitted, the least squares method is an
descriptive method.

18. The results of the method of least squares are most satisfactory.
19. Least square method can be used to fit growth curves.
20. Least square method estimate values only in the immediate future or past.

Case Study Average Growth Rate

T observations for ten weeks.
he weights (in lbs.) of a newly born calf are taken at weekly intervals. Below are the

Age(X weeks) : 1 2 3 4 5 6 7 8 9 10
Weight(Y lbs.) : 52.5 58.7 65.0 70.2 75. 4 81.1 87.2 95.5 102.2 108. 4
Let Y = a + bu, where u = 2X - 11. Use normal equations to estimate a and b. Use these values
to obtain the line of best fit of Y on X and write down the average rate of growth of weight
of the calf per week.

9.3 Summary

Regression of Y on X

XY nX Y n XY X Y
Regression coefficient: b 2
X 2 nX 2 n X 2 X

Cov X ,Y
Also b 2 r Y
X X
Change of scale and origin:

X A Y B k n uv u v
If u and v , then b
h h h n u 2 u 2

Constant term: a Y bX
Alternative form of regression equation:

Y Y X X or Y Y r Y X X
C C
X

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