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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.

PLS ANSWER CORRECTLY WITH AN EXPLANATION

Respuesta :

avgregorytx

Answer:

y = 0.126X - 7.119

8.63

Step-by-step explanation:

X = year, we subtract the year in the data from 1900 ;

So for the years we have :

78,79,80,90,91,96,97,107,108,109

Using technology to fit the data above, the regression model obtained is ;

y = 0.126X - 7.119

Where x = years

y = minimum hourly wage

The minimum hourly wage in 2025

Year = x = 2025 - 1900 = 125 years

y = 0.126(125) - 7.119

y = 8.631

Predicted Minimum hourly wage = 8.63

francocanacari

The estimated minimum wage for 2025 is $ 13.75.

Taking into account the wage data, to determine the equation that models the wage increase and estimate the minimum hourly wage of a U.S. worker in 2025 the following calculations must be performed:

  • 1978 = $ 2.65
  • 1979 = $ 2.90
  • 1980 = $ 3.35
  • 1990 = $ 3.80
  • 1991 = $ 4.25
  • 1996 = $ 4.75
  • 1997 = $ 5.15
  • 2007 = $ 5.85
  • 2008 = $ 6.55
  • 2009 = $ 7.25

  • 2.65 = 100
  • 7.25 = X
  • 725 / 2.65 = 273.58

  • 173.58 / (2009-1978) = X
  • 173.58 / 31 = X
  • 5.6 = X

  • (2025 - 2009) x 5.6 = 89.6  
  • 100 = 7.25
  • 189.6 = X
  • 189.6 x 7.25 / 100 = X
  • 13.75 = X

Therefore, the estimated minimum wage for 2025 is $ 13.75.

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