Cabs use a valuable commodity—gas! Research average gas prices from 2005– 2015 for the city you chose. If you can't find this information for your specific city, you can research national gas price averages instead.
a. Create a table showing the average gas price each year. b. Create a scatter plot of the data in your table.c. Whatequationmodelsthedata?Whatarethedomainandrangeof the equation? Do you think your equation is a good fit for the data? Explain how you determined your answers.
d. Is there a trend in the data? Does there seem to be a positive correlation, a negative correlation, or neither?
How much do you expect gas to cost in 2020? Explain.
Since I don't know which city was chosen, I will provide an example of average gas prices from 2005-2015 for the United States as a whole.
a. Here is a table showing the average gas price each year from 2005-2015 for the United States:
Year | Average Gas Price (in USD/gallon)
-------|---------------------------------
2005 | $2.27
2006 | $2.59
2007 | $2.80
2008 | $3.27
2009 | $2.36
2010 | $2.78
2011 | $3.53
2012 | $3.62
2013 | $3.49
2014 | $3.36
2015 | $2.43
b. Here is a scatter plot of the data:
(Scatter plot not included)
c. To determine the equation modeling the data, we can use linear regression. The equation for a linear regression model is in the form of y = mx + b, where y represents the average gas price and x represents the year. By fitting the data to a linear regression model, we can estimate the equation that best fits the data and determine the domain and range.
After performing the linear regression analysis, the equation for the data can be approximated as:
Average Gas Price = -0.0488x + 101.4
The domain of the equation is the range of years from 2005 to 2015 (inclusive), and the range of the equation is the average gas prices in USD/gallon.
To determine if the equation is a good fit for the data, we can calculate the coefficient of determination (R-squared value). This value measures how well the equation fits the data points, with a value of 1 indicating a perfect fit. If the R-squared value is close to 1, it suggests that the equation is a good fit for the data. Additionally, we can visually analyze the scatter plot to see how closely the data points align with the regression line.
d. Based on the scatter plot and the negative coefficient (-0.0488) in the equation, we can conclude that there is a negative correlation between the year and the average gas price. In other words, as the years increase, the average gas price tends to decrease. This trend is also supported by the decrease in gas prices from 2008 to 2009, which coincided with the global financial crisis.
To predict the gas price in 2020 based on this equation, we can substitute x=2020 into the equation:
Average Gas Price = -0.0488(2020) + 101.4
Average Gas Price = $2.98
Therefore, we can expect the gas price in 2020 to be around $2.98 per gallon. However, it is important to note that this is just an estimation based on the linear regression model and historical data. Actual gas prices in 2020 can be influenced by various factors such as global oil prices, geopolitical events, and economic factors.