1. The table shows the minimum wage rates for the United States during different years.

Year 1978 1979 1980 1990 1991 1996 1997 2007 2008 2009

Minimum hourly wage ($) 2.65 2.90 3.35 3.80 4.25 4.75 5.15 5.85 6.55 7.25

(a) Write the least squares regression equation that models the data. Let x = time in years since 1900 and let y = minimum hourly wage.

(b) Use the equation to estimate the minimum hourly wage of a U. S. worker in 2025. Show your work.

The regression equation will be given by:

m (x-x1) = y-y1

where:

m = (y1-y) / (x1-x)

thus from the data given we shall have:

m = (7.25-3.8) / (2009-1990) = 3.45/19=0.182

thus the equation will be:

taking 1990 as the zero we shall have:

0.182 (x-0) = y-3.8

thus

y=0.182x+3.8

Thus the equation is:

y=0.182x+3.8

b] Use the equation to estimate the minimum hourly wage of a U. S. worker in 2025. Show your work.

x=2025-1990=35

thus

y=0.182 (25) + 3.8

y=6.37+3.8

y=10.17

Hence the hourly minimum wage will be $10.17