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 = 1780 + 1.5x. (a) What is the expected value of 28-day strength when accelerated strength = 2550? (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 110 psi? d) By how much can we expect 28-day strength to change when accelerated strength decreases by 110 psi?

Explanation / Answer

y = 1780 + 1.5x

1)

Put x = 2550
y = 1780 + 1.5 * 2550
= 5605

2)
When x increasd by 1 , the 28 day standard cured strength increased by 1.5 * 1 = 1.5

3)
When x increasd by 1 , the 28 day standard cured strength increased by 1.5 * 110 = 165

4)
When x decreasd by 1 , the 28 day standard cured strength decreased by 1.5 * 110 = 165

  

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