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.
7. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither?
1. The average gas price for 2010 is $2.22.
2. In order to accurately represent the average gas prices from 2005 to 2015, a scatter plot would have years on the x-axis and gas prices on the y-axis. Each data point would then be plotted based on its respective year and gas price. The scatter plot would show a general trend of how gas prices have changed over the years.
3. To find the linear regression equation, we would use the given data points from 2002 to 2011. Using a linear regression calculator or software, we would input the data points and obtain the equation. The linear regression equation would give us the line of best fit through the data points.
4. The domain of the linear regression equation would be the range of years included in the data, which is from 2002 to 2011. In interval notation, this would be [2002, 2011].
5. The range of the linear regression equation would be the lowest and highest possible gas prices based on the line of best fit. Without knowing the equation, we cannot provide a specific range in interval notation.
6. The answer to question 1 is determined by simply looking at the table and finding the gas price for 2010. For question 2, a scatter plot accurately represents the data by plotting the points according to their respective years and gas prices. For question 3, a linear regression calculator or software is used to find the equation that best fits the data points. For questions 4 and 5, the domain and range of the linear regression equation can be determined based on the range of years in the data and the line of best fit.
7. Based on the data presented, there seems to be a general increasing trend in gas prices over the years. This indicates a positive correlation, as the gas prices are generally getting higher over time. However, the relationship may not be perfectly linear, as there are slight fluctuations in the prices from year to year.