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
Cabs use a valuable commodity-gas!
13Find the linear regression equation that models the data above
To find the linear regression equation that models the data above, we can use the least squares regression method.
First, we'll need to find the average gas price for each year. We can do this by adding all the gas prices for each year and dividing by the number of years.
2002-2006: (0.70 + 1.04 + 1.15 + 1.38 + 1.86) / 5 = $1.206
2007-2011: (1.70 + 2.55 + 1.29 + 2.22 + 2.56) / 5 = $2.064
Next, we'll calculate the average year. We can do this by adding up all the years and dividing by the number of years.
2002-2006: (2002 + 2003 + 2004 + 2005 + 2006) / 5 = 2004
2007-2011: (2007 + 2008 + 2009 + 2010 + 2011) / 5 = 2009
Now we can calculate the slope (m) of the regression line using the formula:
m = (average price for 2007-2011 - average price for 2002-2006) / (average year for 2007-2011 - average year for 2002-2006)
m = ($2.064 - $1.206) / (2009 - 2004) = $0.374
Finally, we can find the y-intercept (b) of the regression line using the formula:
b = average price for 2002-2006 - m * average year for 2002-2006
b = $1.206 - $0.374 * 2004 = $1.206 - $749.896 = -$748.69
Therefore, the linear regression equation that models the data above is:
y = 0.374x - 748.69
where y represents the gas price and x represents the year.