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. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is = 1 + 1X . The time is in minutes and the strength is measured in pounds per square inch, MSE = 0.5, = 30, = 104. Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 4 minutes. The distance value has been found to be equal to 0.17143.

An experiment was performed on a certain metal to determine if the strength is a function of heating time. Partial results based on a sample of 10 metal sheets are given below. The simple linear regression equation is Sigmax^2 = 104. Determine the 95% prediction interval for the strength of a metal sheet when the average heating time is 4 minutes. The distance value has been found to be equal to 0.17143. Sigma X = 30, Y = 1 + 1X . The time is in minutes and the strength is measured in pounds per square inch, MSE = 0.5,

Solution

mean

30/10 =3

then

var=sum(X-mean)² = sum(X² ) -n(mean)²

                            =104 -90=14

then standerd deviation =3.74

standerd deviation/square root(n) =3.74/square root(10) =3.74/3.16 =1.18

then interval is (3-1.18 ,3 +1.18) =(1.82 ,4.18)