AVERAGE GAS PRICES
Columbia, South Carolina
Year
Gas Price
Year
Gas Price
2002
$0.70
2007
$1.70
2003
$1.04
2008
$2.55
2004
$1.15
2009
$1.29
2005
$1.38
2010
$2.22
2006
$1.86
2011
$2.56
Use the linear regression equation to predict how much you expect gas to cost 2025?
To predict the gas price in 2025, we can use the linear regression equation.
First, we need to calculate the slope (m) and y-intercept (b) of the regression line for the given data points. The equation for a regression line is y = mx + b, where y is the gas price and x is the year.
We can use the slope-intercept form of a line to calculate the slope and y-intercept:
m = (Σ(xy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2)
b = (Σy - m(Σx)) / n
where Σxy is the sum of the products of x and y, Σx and Σy are the sums of x and y respectively, Σx^2 is the sum of the squares of x, and n is the number of data points.
Using the given data points, we can calculate the slope and y-intercept:
Σx = 2002 + 2003 + 2004 + 2005 + 2006 + 2007 + 2008 + 2009 + 2010 + 2011 = 20105
Σy = 0.70 + 1.04 + 1.15 + 1.38 + 1.86 + 1.70 + 2.55 + 1.29 + 2.22 + 2.56 = 16.85
Σxy = (2002 * 0.70) + (2003 * 1.04) + (2004 * 1.15) + (2005 * 1.38) + (2006 * 1.86) + (2007 * 1.70) + (2008 * 2.55) + (2009 * 1.29) + (2010 * 2.22) + (2011 * 2.56) = 40289.78
Σx^2 = (2002^2) + (2003^2) + (2004^2) + (2005^2) + (2006^2) + (2007^2) + (2008^2) + (2009^2) + (2010^2) + (2011^2) = 40584595
n = 10
Now, let's plug in the values into the slope and y-intercept formulas:
m = (Σ(xy) - (Σx)(Σy) / n(Σx^2) - (Σx)^2)
= (40289.78 - (20105)(16.85)) / (10(40584595) - (20105)^2)
= (-65459.85) / (40584595 - 40421025)
= (-65459.85) / 163570
≈ -0.40
b = (Σy - m(Σx)) / n
= (16.85 - (-0.40)(20105)) / 10
= (16.85 + 8042) / 10
≈ 805.27 / 10
≈ 80.53
So, the regression equation for the given data points is:
y = -0.40x + 80.53
Using this equation, we can find the predicted gas price for the year 2025 by substituting x = 2025 into the equation:
y = -0.40(2025) + 80.53
= -810 + 80.53
≈ -729.47
Therefore, we would expect the gas price in Columbia, South Carolina in 2025 to be approximately -$729.47.