Association

1. Simple linear regression:
• The dependence of on one or more variables is called
regression
• When we study the dependence of a variable on single
independent variable, it is called simple linear regression or
two variable regression. i.e
1. The height of a child depends on the height of the parents
2. The temperature depends on the shining on the sun.
3. The production of a crop depends on the quality of seed

2. Simple linear regression:
X and Y values
always given in the
data set.

3. Simple linear regression:

4. Simple linear regression:
X 0 1 2 3 4
y 1.0 1.8 3.3 4.5 6.3
Number
of values
X Y Xy
1 0 1 0*1=0
2 1 1.8 1*1.8=1.8
3 2 3.3 2*3.3=6.6
4 3 4.5 3*4.5=13.5
5 4 6.3 6.3*4=25.2
Total

5. Simple linear regression:

6. Correlation coefficient
The quantity r, called the linear correlation coefficient, measure the
strength and direction of a linear relationship b/w two variables. Like X
and Y.
Example:
I. Marks obtained by a student and his/her study hours.
II. Sugar level and exercise time of an individual.
III. Level of uric acid and consumption of red meat.

7. Properties of correlation coefficient
• Range of the r=[-1 to +1 ]
• r>0 it means that variable moves in same direction.
• r<0 it means that variable moves in opposite direction.
• r=0 Their is no any relation b/w two variable.
• r=+1 It means that there is perfect +ve relation.
• r=-1 It means that there is perfect -ve relation.
• 𝑟𝑥𝑦 = 𝑟𝑦𝑥

8. Correlation formula:
𝑟 =
𝑛(σ 𝑋𝑌) − (σ 𝑋)(σ 𝑌)
(𝑛 σ 𝑋2 − σ 𝑋 2) (𝑛 σ 𝑌2 − σ 𝑌 2)

9. Calculate the r b/w the yield of crop and
fertilizer used.
X (fertilizer ) Y (yield ) XY 𝒙𝟐 𝒚𝟐
0 9 0*9=0 𝟎𝟐
=0 𝟗𝟐
=81
1 16 1*16=16 𝟏𝟐
=1 𝟏𝟔𝟐
=?
2 25 50 𝟐𝟐
= 𝟒 𝟐𝟓𝟐
=?
3 38 114 𝟑𝟐
= 𝟗 𝟑𝟖𝟐
=?
4 50 200 𝟒𝟐 = 𝟏𝟔 𝟒𝟎𝟐 =?
5 60 300 𝟓𝟐 = 𝟐𝟓 𝟔𝟎𝟐 = 𝟑𝟔𝟎𝟎
15 198 680 55 8506
Total

10. Solution
• 𝑟 =
𝑛(σ 𝑋𝑌)−(σ 𝑋)(σ 𝑌)
(𝑛 σ 𝑋2− σ 𝑋 2)(𝑛 σ 𝑌2− σ 𝑌 2)
• 𝑟 =
6∗680−15∗198
(6∗55− 15 2) (6∗8506− 198 2)
• 𝑟 =
1110
105 ∗(11832)
=
1110
1114.61
= 0.99