Regression analysis is a statistical technique used to determine the relationship between variables. There are two main types: simple linear regression which involves one independent and one dependent variable, and multiple linear regression which involves multiple independent variables and one dependent variable. The regression process fits a linear equation to a set of data points to calculate the coefficients that best represent the strength and direction of the relationship between the variables.

2. INTRODUCTION
Regression analysis is a statistical technique used to determine the relationship
between a dependent variable and one or more independent variables. It is often
used to predict or estimate the value of the dependent variable based on the
values of the independent variables.
The process involves fitting a regression model to the data, which involves
calculating the coefficients that best fit the data. These coefficients represent
the strength and direction of the relationship between the independent and
dependent variables.

3.  Simple Linear Regression: This method involves fitting a linear
equation to a set of data points. It is used when there is a single
independent variable and one dependent variable.
There are two types of regression analysis.
 Multiple Linear Regression: In this method, a linear equation is
fitted to a set of data points with multiple independent
variables and one dependent variable.

4. OVER RUN
1 2
2 5
3 8
4 12
5 14
6 18
7
8
9
X Y
Y
48
44
40
36
32
28
24
20
16
12
8
4
0 1 2 3 4 5 6 7 8 9 10 X
INTERCEPT

5. OVER RUNS
1 2
2 5
3 8
4 12
5 14
6 18
7
8
9
X Y
40
36
32
28
24
20
16
12
8
4
0 1 2 3 4 5 6 7 8 9
RUNS
OVE
R
OVER
X
o Independent variable/Explanatory Variable.
o Used to predict the variable of interest.
o Dependent variable/Explained Variable.
o It is predicted by using explanatory
variable.
RUN Y
Simple Linear
Regression

6. Regression equation of Y on X:
 “a” is Y-intercept” & a constant
 “b” is the “slope” of regression line & a constant.
 “b” represents change in Y variable for a unit change in X
variable.
For determination of “a” & “b” simultaneously
Y = a +
bx
𝜮𝒚 = 𝑵𝒂 + 𝒃𝜮𝑿
𝜮𝒙𝒚 = 𝒂𝜮𝒙 + 𝒃𝜮𝑿𝟐
Regression equation of X on Y: X = a + by
𝜮𝐱 = 𝑵𝒂 + 𝒃𝜮𝒀
𝜮𝒙𝒚 = 𝒂𝜮𝐘 + 𝒃𝜮𝒀𝟐
X = a + by

7. OVER RUN
1 2
2 5
3 8
4 12
5 14
6 18
Regression equation of Y on X:
Y = a +
bx
𝜮𝒚 = 𝑵𝒂 + 𝒃𝜮𝑿….1
𝜮𝒙𝒚 = 𝒂𝜮𝒙 + 𝒃𝜮𝑿𝟐….2
X Y XY 𝑿𝟐 𝒀𝟐
1 2 2 1 4
2 5 10 4 25
3 8 24 9 64
4 12 48 16 144
5 14 70 25 196
6 18 108 36 324
21 59 262 91 757
(59 = 6a + b x 21)......1
(262 = a x 21 + b x 91).....2
(59 = 6a + b x 21)......1 x 7
(262 = a x 21 + b x 91).....2 x 2
413 = 42a + 147b)......3
- 524 = 42a + 182b).....4
-111 = -35b
b =
−𝟏𝟏𝟏
−𝟑𝟓
b = 3.17
59 = 6a + 3.17 x 21
Value of a =
6a = 59 - 66.57 6a = -7.57 a =
−𝟕.𝟓𝟕
𝟔
a = -1.26
X Y

8. Regression equation of Y
on X:
Y = a +
bx
X = 12
Y =
..?
Y = -1.26 + 3.17 x 12 Y = -1.26 + 38.04
Y = 36.78

9. Regression equation of X on Y: X = a + by
𝜮𝐱 = 𝑵𝒂 + 𝒃𝜮𝒀
𝜮𝒙𝒚 = 𝒂𝜮𝐘 + 𝒃𝜮𝒀𝟐
(21 = 6 x a + b x 59)......1
(262 = a x 59 + b x 757).....2
(21 = 6 x a + b x 59)......1 x 59
(262 = a x 59 + b x 757).....2 x 6
1239 = 354a + 3481b
-1572 = 354a + 4542b
-333 = -1061b
b =
𝟑𝟑𝟑
𝟏𝟎𝟔𝟏
b = 0.314
Value of a =
21 = 6 x a + 0.314 x 59 6a = 21- 18.526 6a = 2.474 a =
𝟐.𝟒𝟕𝟒
𝟔
a = 0.412

10. Regression equation of X
on Y:
X = …?
Y = 27
X = 0.412 + 0.314 x 27 X = 0.412 + 8.478
Y = 8.89/
approx. 9
over
X = a + by