An experiment was performed on a certain metal to determine if the strength is a

Question

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 = 600, XY = 304

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 and check the relation between coefficient of correlation and coefficient of determination. Finally, perform the test of significance of the slope coefficient.

Explanation / Answer

Solution:

Given X = 40,X2 = 200, Y = 80, Y2 = 600, XY = 304

now slope y= a+bx

b= (304/20 - 40/20 * 80/20 ) / (200/20 - (40/20)^2) = 7.2 / 6 = 1.2

a = 80/20 - 1.2 *40/20 = 1.6

y_predict at 3 hours = 1.6 + 1.2*3 = 5.2

r = 304/20 - 40/20 * 80/20 / sqrt ((200/20 - (40/20)^2) (600/20 - (80/20)^2)) = 7.2/9.1652 = 0.7856

r_square = 1.2*sqrt((1/20) * 200 - (40/20)^2) / sqrt(600/20 - (80/20)^2 = 2.939/ 3.74 = 0.786

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