Question

diameter	age
1.8	4
1.8	5
2.2	8
4.4	8
6.6	8
4.4	10
7.7	10
10.8	12
7.7	13
5.5	14
9.9	16
10.1	18
12.1	20
12.8	22
10.3	23
14.3	25
13.2	28
9.9	29
13.2	30
15.4	30
17.6	33
14.3	34
15.4	35
11	38
15.4	38
16.5	40
16.5	42

The data table below gives the diameter and age of 27 trees that were cut down to make open space for a playground. Diameter (inches) 1.8 1.8 2.2 4.4 6.6 4.4 7.7 10.8 Age (years) 4 Diameter (inches) 10.3 14.3 13.2 9.9 13.2 15.4 17.6 14.3 15.4 11.0 15.4 16.5 16.5 Age (years) 23 25 28 29 30 30 10 10 12 13 14 16 18 20 34 35 38 38 40 5.5 9.9 10.1 12.1 12.8

Create a linear model for solving the slope and intercept of the best fitting straight line by hand. Show all work

Answer 1

	Diameter (X)	Age (Y)	X * Y	X2
	1.8	4	7.2	3.24
	1.8	5	9	3.24
	2.2	8	17.6	4.84
	4.4	8	35.2	19.36
	6.6	8	52.8	43.56
	4.4	10	44	19.36
	7.7	10	77	59.29
	10.8	12	129.6	116.64
	7.7	13	100.1	59.29
	5.5	14	77	30.25
	9.9	16	158.4	98.01
	10.1	18	181.8	102.01
	12.1	20	242	146.41
	12.8	22	281.6	163.84
	10.3	23	236.9	106.09
	14.3	25	357.5	204.49
	13.2	28	369.6	174.24
	9.9	29	287.1	98.01
	13.2	30	396	174.24
	15.4	30	462	237.16
	17.6	33	580.8	309.76
	14.3	34	486.2	204.49
	15.4	35	539	237.16
	11	38	418	121
	15.4	38	585.2	237.16
	16.5	40	660	272.25
	16.5	42	693	272.25
Total	280.8	593	7484.6	3517.64

Equation of linear model

Y = a + bx

Where, a :- Y intercept

b :- Slope of the equation line

To calculate

Y = a + bx

Y = - 0.9744 + 2.2055 X

Age paramenter is taken on Y axis and diameter parameter is taken in X axis and plotted the data points accordingly.