Intercept Calculation – Simple Linear Regression Analysis

1. The equation of regression line

An equation of a dependent variable predicted by an independent variable consists of two parameters, a regression slope and intercept. This concept is likely to be introduce during the JC H2 mathematics class.

2. To determine the regression slope, the following formula can be used:

Regression Slope = Covariance(x,y)/Variance(x)

3. On the other hand, the intercept of the regression line is defined as:

Intercept = (Mean of y) – (Regression Slope)*(Mean of x)

Exercise

Calcuate the intercept of the following regression lines.

Question 1

Y3	X3
12	14
10	14
14	11
13	15
15	10
10	14
14	11
11	12
10	12
13	10
11	13
12	12
15	14
12	11
13	10
14	13
14	12
15	13
15	13
13	11
11	13

Question 2

Y4	X4
14	13
11	11
15	15
13	12
10	12
13	15
15	12
13	12
14	15
10	15
15	12
10	12
11	14
15	11
15	10
12	12
10	11
13	12
12	15
15	14
15	12

Question 3

Y1	X1
12	13
13	12
12	15
12	13
11	10
13	13
12	12
13	15
12	14
11	10
13	11
12	11
11	14
10	14
11	10
14	10
13	14
15	11
15	10
14	10
12	11

Question 4

Y2	X2
12	13
11	10
12	12
10	15
14	14
11	11
14	10
11	10
13	15
11	11
13	12
12	11
14	10
13	13
12	12
13	10
12	15
11	14
10	12
12	13
13	11

Question 5

Y5	X5
12	11
10	15
13	11
14	14
11	11
15	15
13	15
14	15
12	12
12	15
11	13
10	10
15	13
15	13
13	11
11	13
13	13
14	10
12	13
14	13
10	11

Question 6

Y6	X6
11	11
10	13
10	12
10	12
11	15
10	10
15	14
13	12
13	15
13	12
12	15
14	15
14	14
14	15
12	14
13	11
13	14
10	15
12	13
15	11
14	11

Answer

16.123
13.302
14.734
13.111
9.206
10.577

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Y3	X3
12	14
10	14
14	11
13	15
15	10
10	14
14	11
11	12
10	12
13	10
11	13
12	12
15	14
12	11
13	10
14	13
14	12
15	13
15	13
13	11
11	13

Y4	X4
14	13
11	11
15	15
13	12
10	12
13	15
15	12
13	12
14	15
10	15
15	12
10	12
11	14
15	11
15	10
12	12
10	11
13	12
12	15
15	14
15	12

Y1	X1
12	13
13	12
12	15
12	13
11	10
13	13
12	12
13	15
12	14
11	10
13	11
12	11
11	14
10	14
11	10
14	10
13	14
15	11
15	10
14	10
12	11

Y2	X2
12	13
11	10
12	12
10	15
14	14
11	11
14	10
11	10
13	15
11	11
13	12
12	11
14	10
13	13
12	12
13	10
12	15
11	14
10	12
12	13
13	11

Y5	X5
12	11
10	15
13	11
14	14
11	11
15	15
13	15
14	15
12	12
12	15
11	13
10	10
15	13
15	13
13	11
11	13
13	13
14	10
12	13
14	13
10	11

Y6	X6
11	11
10	13
10	12
10	12
11	15
10	10
15	14
13	12
13	15
13	12
12	15
14	15
14	14
14	15
12	14
13	11
13	14
10	15
12	13
15	11
14	11

Y3	X3
12	14
10	14
14	11
13	15
15	10
10	14
14	11
11	12
10	12
13	10
11	13
12	12
15	14
12	11
13	10
14	13
14	12
15	13
15	13
13	11
11	13

Y4	X4
14	13
11	11
15	15
13	12
10	12
13	15
15	12
13	12
14	15
10	15
15	12
10	12
11	14
15	11
15	10
12	12
10	11
13	12
12	15
15	14
15	12

Y1	X1
12	13
13	12
12	15
12	13
11	10
13	13
12	12
13	15
12	14
11	10
13	11
12	11
11	14
10	14
11	10
14	10
13	14
15	11
15	10
14	10
12	11

Y2	X2
12	13
11	10
12	12
10	15
14	14
11	11
14	10
11	10
13	15
11	11
13	12
12	11
14	10
13	13
12	12
13	10
12	15
11	14
10	12
12	13
13	11

Y5	X5
12	11
10	15
13	11
14	14
11	11
15	15
13	15
14	15
12	12
12	15
11	13
10	10
15	13
15	13
13	11
11	13
13	13
14	10
12	13
14	13
10	11

Y6	X6
11	11
10	13
10	12
10	12
11	15
10	10
15	14
13	12
13	15
13	12
12	15
14	15
14	14
14	15
12	14
13	11
13	14
10	15
12	13
15	11
14	11

Y3	X3
12	14
10	14
14	11
13	15
15	10
10	14
14	11
11	12
10	12
13	10
11	13
12	12
15	14
12	11
13	10
14	13
14	12
15	13
15	13
13	11
11	13

Y4	X4
14	13
11	11
15	15
13	12
10	12
13	15
15	12
13	12
14	15
10	15
15	12
10	12
11	14
15	11
15	10
12	12
10	11
13	12
12	15
15	14
15	12

Y1	X1
12	13
13	12
12	15
12	13
11	10
13	13
12	12
13	15
12	14
11	10
13	11
12	11
11	14
10	14
11	10
14	10
13	14
15	11
15	10
14	10
12	11

Y2	X2
12	13
11	10
12	12
10	15
14	14
11	11
14	10
11	10
13	15
11	11
13	12
12	11
14	10
13	13
12	12
13	10
12	15
11	14
10	12
12	13
13	11

Y5	X5
12	11
10	15
13	11
14	14
11	11
15	15
13	15
14	15
12	12
12	15
11	13
10	10
15	13
15	13
13	11
11	13
13	13
14	10
12	13
14	13
10	11

Y6	X6
11	11
10	13
10	12
10	12
11	15
10	10
15	14
13	12
13	15
13	12
12	15
14	15
14	14
14	15
12	14
13	11
13	14
10	15
12	13
15	11
14	11