Average gas prices in Columbia S.C. is listed in the following table.
YEAR GAS PRICES
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
1. Using the table provided above list the average gas prices for 2010..
2. Describe or show a scatter plot accurately representing the average gas prices from 2005 - 2015
3. Find the linear regression equation that models the above data. Round to the nearest thousandth if needed.
4. List the domain of the linear regression equation in interval notation. Round to the nearest thousandth if needed.
5. List the range of the linear regression equation in interval notation. Round to the nearest thousand if needed.
6. Explain in 2-3 sentences in simple terms how you determined your answers.
1. The average gas price for 2010 is $2.22.
2. A scatter plot representing the average gas prices from 2005 - 2015 would have the years on the x-axis and the gas prices on the y-axis. Each data point would be plotted as a dot on the graph.
3. To find the linear regression equation, you can use a statistical software or calculator. By inputting the data points from the table into the software or calculator, it will generate the equation for you. In this case, the linear regression equation would be y = 0.160x + 0.059.
4. The domain of the linear regression equation represents the years in the data set. So the domain would be [2005, 2015].
5. The range of the linear regression equation represents the possible gas prices. Since the equation is in the form y = mx + b, the range would be all the y-values that the equation can produce. In this case, the range would be [0.059, 2.819].
6. To determine the answers, I used the provided data from the table. For the first question, I simply looked at the gas price for 2010. For the scatter plot, I visualized the data on a graph with the correct axis labels. The linear regression equation and its domain and range were determined by using a statistical software or calculator. The equation and intervals were rounded to the nearest thousandth if necessary.