An article on estimating 28-day strength of concrete considered regressing y = 2

Question

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 = 1820 + 1.5x.

(a) What is the expected value of 28-day strength when accelerated strength = 2440?
psi

(b) By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi?
psi

(c) By how much can we expect 28-day strength to change when accelerated strength increases by 50 psi?
psi

(d) By how much can we expect 28-day strength to change when accelerated strength decreases by 50 psi?
psi

Explanation / Answer

y = 1820 + 1.5x

a) x = 2440

y = 1820 + 1.5 * 2440 = 5480

b) So, we can expect 28-day strength to increase by 1.5 psi when accelerated strength increases by 1 psi

c) So, we can expect 28-day strength to increase by 50 * 1.5 = 75 psi when accelerated strength increases by 50 psi

d) So, we can expect 28-day strength to decrease by 50 * 1.5 = 75 psi when accelerated strength decreases by 50 psi

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