What would be the closest to the population in 2005?

Question

A town planner models the population of a town using a linear function f(t), where t represents the number of years after 2005. The table shows the population of the town at different years.

 

Which value is closet to the population in 2005, predicted by f(t) ?

a	43,700
b	45,700
c	47,700
d	42,700
e	44,700
f	46,700

Answer 1

ŷ = 1012.42105t + 44643.52632

is the equation of the least squares regression trend line....

since t is the # of years since 2005, the year 2005 forces t=0

which means we are trying to the y-intercept

when t=0, y = 44643.52632; that is (0,44643.52632) IS the y-intercept

option E is the closest at 44700

Answer 2

The population increases by 994 each year - (51,691 - 48,709) / (7 - 3)

After 2005 there were three years of increases - 2,982

48,709 - 2982 = 45,727