Answer :
Answer:
$6.58
Step-by-step explanation:
Here’s the given data:
Year
Minimum Hourly Wage ($)
2000
5.15
2001
5.15
2002
5.15
2003
5.15
2004
5.15
2005
5.15
2006
5.15
2007
6.85
2008
7.00
2009
7.30
2010
7.30
2011
7.40
2012
7.70
2013
7.85
2014
7.95
2015
8.10
2016
8.10
2017
8.15
2018
8.30
2019
8.55
2020
8.70
2021
8.80
2022
8.80
2023
8.80
2024
8.80
To create a linear regression equation, we’ll find the slope and y-intercept. Let’s calculate:
Calculate the average of the x-values (years) and the y-values (minimum hourly wage):
xˉ=n1i=1∑nxi
yˉ=n1i=1∑nyi
where (n) is the number of data points.
Calculate the slope ((m)):
m=∑i=1n(xi−xˉ)2∑i=1n(xi−xˉ)(yi−yˉ)
Calculate the y-intercept ((b)):
b=yˉ−mxˉ
Now let’s compute the values:
(n = 25)
(\bar{x} = \frac{1}{25} \sum_{i=1}^{25} x_i = 2012)
(\bar{y} = \frac{1}{25} \sum_{i=1}^{25} y_i = 7.98)
Using the formulas above, we find:
(m \approx 0.035)
(b \approx -70.5)
Therefore, the linear regression equation is:
[ y = 0.035x - 70.5 ]
Now let’s predict the minimum hourly wage in 2032:
(x = 2032 - 2000 = 32)
(y = 0.035 \cdot 32 - 70.5 \approx 6.58)
Rounded to the nearest cent, the predicted minimum hourly wage for an Ohio worker in 2032 is approximately $6.58.
