Question 1188967
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.


<a href = "https://byjus.com/maths/linear-regression/" target = "_blank">https://byjus.com/maths/linear-regression/</a>


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