average gas prices
columbia sc
year 2002 $0.70
year 2003 $1.04
year 2004 $1.15
year 2005 $1.38
year 2006 $ 1.86
year 2007 $1.70
year 2008 $ 2.55
year 2009 $1.29
year 2010 $2.22
year 2011 $2.56
11. Using the table provided above, list the average gas price for 2010.
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The average gas price for 2010 in Columbia, SC was $2.22.
Find the linear regression equation that models the data above. Round to the nearest thousandth
To find the linear regression equation that models the data, we need to determine the line of best fit.
First, we calculate the average values of the x and y variables:
x̄ = (2002+2003+2004+2005+2006+2007+2008+2009+2010+2011) / 10 = 2006.5
ȳ = (0.70+1.04+1.15+1.38+1.86+1.70+2.55+1.29+2.22+2.56) / 10 = 1.703
Next, we calculate the sum of the products of the x and y variables:
Σ(xy) = (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) = 40,667.02
We also calculate the sum of the squares of the x variables:
Σ(x²) = (2002²) + (2003²) + (2004²) + (2005²) + (2006²) + (2007²) + (2008²) + (2009²) + (2010²) + (2011²) = 40,474,490
Using the formulas for the slope and y-intercept of the line of best fit:
Slope (b) = (Σ(xy) - (n)(x̄ȳ)) / (Σ(x²) - (n)(x̄²))
Y-intercept (a) = ȳ - (b)(x̄)
Plugging in the values:
n = 10
b = (40,667.02 - (10)(2006.5)(1.703)) / (40,474,490 - (10)(2006.5)²)
a = 1.703 - (b)(2006.5)
After calculating, we find:
b ≈ 0.487
a ≈ -970.769
Therefore, the linear regression equation that models the data is:
y ≈ 0.487x - 970.769
14. List the domain of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
The domain of the linear regression equation is the set of all possible input values, or x-values.
Since the linear regression equation is a line, the domain is the set of all real numbers. In interval notation, this can be expressed as (-∞, ∞).