Question

As Concrete cures, it gains strength. The following data represent the 7-day and 28-day strength in psi of a certain type of concrete. Conduct regression analysis for the following data and comment on the coefficient of determination value. Calculate the 28th day strength for the concrete with seventh day strength of 4 psi

7-day 28-day strength, strength, X y 2,300 4,070 3,390 5,220 2,430 4,640 2,890 4,620 3,330 4,850 2,480 4,120 3,380 5,020 2,660 4,890 2,620 4,190 3,340 4,630

Answer 1

Using the method of least squares, the estimated regression line is given by

Y=a+bX, where a is the intercept and b is the slope estimate.

slope = b = average(cy) – average(2) * averagely) [average(22) - (average(2))2]

and intercept =a = average(y) - b*average(x)

Substituting the values, we get , b= -0.713 and a=131.355

Thus, the regression line is Y= 131.355 -0.713X

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Using the method of least squares, the estimated regression line is given by

Y=a+bX, where a is the intercept and b is the slope estimate.

slope = b = average(cy) – average(2) * averagely) [average(22) - (average(2))2]

and intercept =a = average(y) - b*average(x)

Substituting the values, we get , b= 0.676 and a=2675.562

Thus, the regression line is Y= 2675.562 + 0.676X

the correlation coefficient is calculated using the formula

$r = \frac{average(xy)-average(x)*average(y)}{\sqrt{[average(x^2)-(average(x))^2]*[average(y^2)-(average(y))^2]}}$Substituting the values, we get r = 0.7584

The coefficient of determination is given by r^2 = 0.7584^2 = 0.5751

i.e the model explains about 57.5% of the total variation.