An article on estimating 28-day strength of concrete considered regressing y = 28-day standard-cured strength (psi) against x = accelerated strength (psi). Suppose the equation of the true regression line is y = 1,760 + 1.2x. (a) What is the expected value of 28-day strength when accelerated strength = 2,520? (b) By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi? (c) By how much can we expect 28-day strength to change when accelerated strength increases by 80 psi? (d) By how much can we expect 28-day strength to change when accelerated strength decreases by 80 psi? Step 1 (a) What is the expected value of 28-day strength when accelerated strength = 2,520? We are given the accelerated strength, x = 2,520 psi. Use this value of x in the given regression line equation in order to find the expected value of 28-day strength when the accelerated strength is 2,520 psi. y = 1,760 + 1.2x = 1,760 + 1.2 2520 2,520 = 4784 4,784 The expected value of 28-day strength (in pounds per square inch) with an accelerated strength of 2,520 psi is 4784 4,784 psi. Step 2 (b) By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi? Recall the formula for the regression line : * = Bo + BIX , where Bo is the y-intercept and B, represents the slope, which is, by definition, the change in y for every one unit increase in x. Recall that we were previously given the regression equation y = 1,760 + 1.2x. We can apply this definition of slope to this situation by saying when accelerated strength increases by 1 psi, the expected change in 28-day strength (in pounds per square inch) is psi