Answer:
y = 0.834X - 1.58015
Slope = 0.8340 ; Intercept = - 1.5802
y = 40.9539
19.93
0.9765
Explanation:
X: Rainfall volume
6
12
14
16
23
30
40
52
55
67
72
81
96
112
127
Y : Runoff
4
10
13
14
15
25
27
48
38
46
53
72
82
99
100
The scatterplot shows a reasonable linear trend between the Rainfall volume and run off.
The estimated regression equation obtained using a linear regression calculator is :
y = 0.834X - 1.58015
y = Runoff ; x = Rainfall volume
Slope = 0.8340 ; Intercept = - 1.5802
Point estimate for Runoff, when, x = 51
y = 0.834X - 1.58015
y = 0.834(51) - 1.58015
y = 40.95385
y = 40.9539
d.)
Point estimate for standard deviation :
s = 5.145
σ = s * √n
σ = √15 * 5.145
= 19.93
e.)
r² = Coefficient of determination gives the proportion of explained variance in Runoff due to the regression line. From the model output, the r² value = 0.9765. Which means That about 97.65% Runoff is due to Rainfall volume.
