This is about average gas prices from 2005-2015
2005 - $2.27
2006 - $2.57
2007 - $2.80
2008 - $3.25
2009 - $2.35
2010 - $2.78
2011 - $3.52
2012 - $3.62
2013 - $3.51
2014 - $3.36
2015 - $2.43
c. What equation models the data? What are the domain and range of
the equation? Do you think your equation is a good fit for the data?
Explain how you determined your answers.
How do I do this?
check the changes each year:
+0.30
+0.23
+0.45
-0.90
+0.37
+0.74
+0.10
-0.11
-0.15
-0.93
even without doing a regression, it is clear that no straight line can model this set of data with any real accuracy.
But, I guess you can always plug in the data using your regression calculator to find the line of "best" fit.
To determine the equation that models the data, we can use regression analysis. By looking at the given data, the trend seems to be fluctuating, but generally follows an increasing pattern until 2011, after which it starts declining.
One possible equation that could model the data is a cubic equation of the form:
𝑦 = 𝑎𝑥^3 + 𝑏𝑥^2 + 𝑐𝑥 + 𝑑
Where:
- 𝑦 represents the gas prices
- 𝑥 represents the years from 2005 to 2015
To find the coefficients 𝑎, 𝑏, 𝑐, and 𝑑, we can use regression analysis software like Excel or statistical programming languages like Python or R.
To determine the domain of the equation, we look at the years of the given data, which ranges from 2005 to 2015. So, the domain of the equation would be the same, ranging from 2005 to 2015.
To determine the range of the equation, we need to analyze the gas prices. From the given data, the gas prices range from a minimum of $2.27 in 2005 to a maximum of $3.62 in 2012. Therefore, the range of the equation would be the set of gas prices within this range.
As for whether this equation is a good fit for the data, we can evaluate the goodness of fit by examining the coefficient of determination (R-squared value) or by plotting the regression line along with the scatter plot of the data points. A higher R-squared value close to 1 indicates a good fit, while a lower value suggests a less accurate fit. Visual inspection of the plot can also give an indication of how well the equation models the data.
Please note that without actually calculating the equation using regression analysis, we cannot determine with certainty the goodness of fit or the exact values of the coefficients.