Question

Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply. Select all that apply: yˆ=38,000+2500x yˆ=38,000−3500x yˆ=−38,000+2500x yˆ=38,000−1500x

Answer 1

1. yˆ=38,000+2500x a=38000, b=2500

2. .yˆ=38,000−3500x a= 38000,b= -3500

3. yˆ=−38,000+2500x a= -38000,b= 2500

4. yˆ=38,000−1500x    a= 38000,b= -1500

Rgression equation y on x

y =population

x = number of years

There is positive correlation between population &number of years

So b (regression coefficient) can not be negative so option 2,4 are not possible

At origin year x=0

putting x=0 in 1 & 3 we get

y = 38000

y = -38000 At origin year population can not be negative

so option 1 is feasible i.e.

yˆ=38,000+2500x is feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015.