So I already made a scatter plot for this data and talked about trends and negative or positive correlations but I have no clue what this question is asking
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.
Can someone please explain to me how I should do this and what it means?
To answer this question, you need to find an equation that models the data. You can do so by analyzing the given data points for average gas prices from 2005-2015.
To find a suitable equation, you can consider various mathematical models or regression techniques such as linear regression, exponential regression, or polynomial regression. Each model will have different equations, and you need to determine which one provides the best fit for the data.
One approach is to plot a scatter plot of the data points and visually examine the trend. Based on your previous analysis, you mentioned trends and negative or positive correlations, which indicates that you have already constructed a scatter plot. This is a good starting point.
Now, look at the scatter plot you created. Consider whether the data points follow a linear, exponential, or polynomial pattern. A linear pattern shows a straight-line relationship, an exponential pattern shows a curved line increasing or decreasing rapidly, and a polynomial pattern shows a curve with gradual changes.
Based on the scatter plot, you can analyze the general trend or shape of the data points and determine which model might be the best fit. Once you decide on a model, you can use regression techniques or software tools to find the equation that best represents the relationship between the independent variable (years) and the dependent variable (average gas prices).
The domain of the equation will be the range of years you have considered, which is 2005 to 2015 in this case. The range of the equation will be the possible range of average gas prices, which you can determine based on the lowest and highest values in the given data.
Finally, you should consider whether the equation you obtained is a good fit for the data. This can be done by evaluating the residuals (the differences between the predicted values from the equation and the actual data points) and calculating various statistical measures like R-squared (coefficient of determination), mean squared error, or other error metrics. These measures will help you assess how well the equation represents the given data.
In summary, to answer the question, you need to determine which equation models the data best. This is done by analyzing the scatter plot, choosing an appropriate model (e.g., linear, exponential, or polynomial), finding the equation, determining the domain and range of the equation, and assessing the goodness of fit using statistical measures.