Question 1188967: For 10 observations on price (X) and supply (Y) the following data were
obtained (in appropriate units):
∑X = 130, ∑Y = 220, ∑X
2 = 2288, ∑Y
2 = 5506 and ∑XY = 3467.
Obtain the line of regression of Y on X and estimate the supply when the price is 16
units, and find out the standard error of the estimate.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i will attempt to answer most of this, if not all.
you are given:
sum(x) = 130
sum(y) = 220
sum(x^2) = 2288
sum(y^2) = 5506
sum(xy) = 3467
the regression equation is y = a + b * x
there are formulas to derive a and b.
they are:
a = (sum(y)*sum(x^2)-sum(x)*sum(xy))/(n*sum(x^2)-sum(x)^2)
b = (n*sum(xy)-sum(x)*sum(y))/(n*sum(x^2)-sum(x)^2)
n is the number of (x,y) data points in the data set.
your solution is that the line of regression is equal to:
y = 8.804347826 + 1.015050167 * x
when x is equal to 16, y is equal to 25.0451505.
here's a reference on the formulas used to get y = a + b * x regression equation.
https://byjus.com/maths/linear-regression/
i had some difficulty understanding how to derive the standard error.
i will look at that again to see if it can be derived from the data presented.
i will do that by tomorrow morning or the next morning after that.
stay tuned.
please send reply with your email so i can let you know when i have the answer.
just a reply through algebra.com should be enough.
theo
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