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1. Simple Linear Regression
• Regression Analysis is a procedure of functional
relationship used for prediction (Ex: Relationship
between Income and Consumption or Salt in-
take and Blood Pressure…)
• Most popular technique used for forecasting
• In Simple Regression, we develop the functional
relationship between two variables say X and Y
where the variable X influences the value of Y,
then X is called the independent variable and Y
is a dependent variable

2. Regression Equation Y on X :
• Y = a + bX
• (Y-Y) = byx (X-X)
• byx Regression Coefficient of Y on X
• Byx = n. ε xy - ε x. ε y
n ε x2 – (ε x)2

3. Regression Equation X on Y :
• X = a + bY
• (X-X) = bxy (Y-Y)
• bxy Regression Coefficient of Xon Y
• Byx = n. ε xy - ε x. ε y
n ε y2 – (ε y)2

4. X: 6 2 10 4 8
Y: 9 11 5 8 7
For the data given, Obtain two Regression
Equations:
• Regression Equation Y on X : Y = a + bX
• (Y-Y) = byx (X-X)
• byx Regression Coefficient of Y on X
• Byx = n. ε xy - ε x. ε y
n ε x2 – (ε x)2

5. X Y XY X2 Y2
6 9 54 36 81
2 11 22 4 121
10 5 50 100 25
4 8 32 16 64
8 7 56 64 49
εX =30 εY =40 εxY =214 εX2 =220 εY2 =340

6. • Byx = n. ε xy - ε x. ε y
n ε y2 – (ε y)2
= (5 X 214) – (30 X 40)
(5 X 220) – (30)2
= 1070 – 1200 = - 130 = - 0.65
1100 – 900 200
Y on X: