Question

In an area of Russia records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). The data for a 9 year period is as follows:

Rain Fall, x 13.1 11.4 16.0 15.1 21.4 12.9 9.6 18.2 18.6
Yield, y 48.5 44.2 56.8 80.4 47.2 29.9 74.0 74.0 76.8
The Equation of the line of least squares is given as ŷ = -9.12+ 4.38x. What would be the expected number of inches of rain if the yield is 60 bushels of wheat per acre?
(a) 11.62 (b) 64.74 c) 253.68 (d) 15.78 ANS: C Plug y= 60 and solve for x.

Answer 1

Option d.

Explanation:

The equation of the line of least squares is given as

`\hat{y} = -9.12+ 4.38x`

where
`\hat{y}` is the yield of wheat (bushels per acre) and x is the rainfall (in inches).

We need to find the expected number of inches of rain if the yield is 60 bushels of wheat per acre.

Substitute
`\hat{y}=60` in the given equation.

`60= -9.12+ 4.38x`

Add 9.12 on both sides.

`60+9.12=4.38x`

`69.12=4.38x`

Divide both sides by 4.38.

`(69.12)/(4.38)=x`

`x\approx 15.78`

The expected number of inches of rain is 15.78.

Therefore, the correct option is d.