We have the following data from year 0 to year 10:
0 | 6340
1 | 7747
2 | 8777
3 | 9809
4 | 10299
5 | 11083
6 | 12373
7 | 12971
8 | 13128
9 | 13608
10| 14679
To manually compute for the regression line's y-intercept, we need to compute for the following first:
sum of all the x's, sum of all the y's, sum of the squares of x, sum of the product of x and y
Hence, we have the following:
sum(x) = 55
sum(y) = 120814
sum(x^2) = 385
sum(xy) = 690660
The slope-intercept form of an equation is y = mx + b. And to estimate the value of the slope, m, we have
m = [ sum(xy) - sum(x)sum(y)/n ] /[ sum(x^2) - (sum(x))^2/n ], where n is the number of data points
m = [690660 - (55)(120814)/11]/ [385 - (55^2)/11]
m ≈ 787.18
Next, to solve for the y-intercept, we have
b = mean(y) - m*mean(x)
b = 120814/11 - 787.18(55/11)
b ≈ 7047.18
This is the manual calculation for the regression line. This can also be done easily with Excel or other data analysis tools available. The y-intercept can be estimated from the best-fit line equation. Seeing that the value of the y-intercept is close to 7000,
the answer is A: 7000.
