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= 1770 + 1.3x. (a) What is the expected value of 28-day strength when accelerated strength 2570? 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 100 psi? psi (d) By how much can we expect 28-day strength to change when accelerated strength decreases by 100 psi? psi

Explanation / Answer

the regression equation is y=1770+1.3x

a) for x=2570 the predicted y is 1770+1.3*2570=3341

b) the coefficient of strength x is 1.3 , thus if x increases by 1, the 28 day strength increases by 1.3

c) similarly, when x increases by 100, y increases by 1.3*100=130

d) if x decreases by 100, the y decreases by 1.3*100=130 or -130

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