Question

Some Field Experience in the use of an Accelerated Method in 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 =1800 +1.3x.

a.What is the expected value of 28-day strength when accelerated strength= 2500? (2 marks)


b.By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi? (4 marks)


c. Answer part (b) for an increase of 100 psi. (2 marks)


d. Answer part (b) for a decrease of 100 ps

Answer 1

(a) 5,050 psi.

(b) 5,051.3 psi.

(c) 5,180 psi.

(d) 4,920 psi.

Explanation:

The given function is

`y=1800+1.3x`

Where
`x` represents the accelerated strength in psi, and
`y` represents 28-day standard-cured strength in psi.

Part a is about finding the y-value for
`x=2500`

`y=1800+1.3(2500)=1800+3250=5,050`

Therefore, the expected value of 28-day strength when accelerated strength is 2,500, is 5,050 psi.

Part b is about the y-value for
`x=2501`

`y=1800+1.3(2501)=1800+3251.3=5,051.3`

Part c is about the y-value for
`x=2600`

`y=1800+1.3(2600)=1800+3380=5,180`

Part d is about the y-value for
`x=2400`

`y=1800+1.3(2400)=1800+3120=4,920`