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. Use the linear regression equation to predict how much you expect gas to cost in 2025?
1. The average gas price for 2010 is $2.22.
2. Unfortunately, the table only provides data from 2002 to 2011, so there is no information available for 2012 - 2015 to create a scatter plot accurately representing the average gas prices.
3. To find the linear regression equation, I would first plot the given data points on a graph. Then, I would use a linear regression calculator or software to find the equation of the line that best fits the data points. By applying the linear regression method, the equation would be determined.
4. The domain of the linear regression equation would be the range of years for which there is data available. Based on the information provided, the domain would be from 2002 to 2011, which can be expressed in interval notation as [2002, 2011].
5. The range of the linear regression equation would be the range of the gas prices. Since the gas prices go from $0.70 to $2.56 in the data provided, the range can be expressed in interval notation as [$0.70, $2.56].
6. The answer for question 1 is obtained by simply looking at the table provided. Unfortunately, question 2 cannot be answered accurately without data for 2012 - 2015. For question 3, I assumed the use of a linear regression calculator or software to find the equation. Questions 4 and 5 are determined based on the given information about the data range.
7. Since we do not have data for 2012 onwards, we cannot accurately predict the gas price for 2025 using the linear regression equation. Linear regression is based on the existing data and would not be reliable for making predictions beyond the range of the data.