An experiment was performed on a certain metal to determine

An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.
X = 40
X² = 200
Y = 80
Y² = 1120
XY = 460

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation.

Solution

a = (y)*(x^2) - (x)*( xy) / n(x^2)*(x^2) = - 1.....
b= n(xy)-(x)( y) / n(x^2)- (x)^2 = 2.5......
y = -1 +2.5*x....
x=3...y = 6.5..

standard error(x) = 0.83667..
men sq,. error of y= 72..
coeff. of correlation = 0.96825..
coeff. of determination = 0.9375...