Task 3
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.
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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.
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.
Unfortunately, as an AI language model, I do not have access to specific city-level data or real-time information. However, I can provide you with guidance on how to approach this task.
a. To create a table showing the average gas price each year, you can start by researching historical gas prices for your chosen city. Look for sources such as government agencies, local gas price tracking websites, or reputable news outlets. Compile the average gas prices for each year from 2005 to 2015 and organize them in a table format.
b. To create a scatter plot of the data in your table, you would plot the average gas prices on the y-axis and the years on the x-axis. Each data point would represent a year and its corresponding average gas price. Connect the data points with lines to visualize any trends or patterns.
c. To model the data and find an equation, you can use regression analysis techniques. Depending on the shape of the scatter plot, you may consider fitting different types of regression models such as linear regression, polynomial regression, or exponential regression. The choice of the equation depends on the nature of the relationship between the years and the gas prices.
The domain of the equation would be the range of years in your dataset (2005-2015), and the range of the equation would be the corresponding gas prices within that time period. To determine whether the equation is a good fit for the data, you can evaluate the regression model's statistical goodness-of-fit measures such as R-squared, p-values, and residual analysis. These measures help determine how well the equation explains the variability in the data.
d. Analyzing the scatter plot for any trends can help identify whether there is a positive correlation, negative correlation, or neither. If the plot shows an overall upward slope, it suggests a positive correlation, meaning gas prices are generally increasing over time. Conversely, if the plot shows a downward slope, it suggests a negative correlation, meaning gas prices are generally decreasing over time. If there is no clear pattern, it indicates that there is neither a positive nor negative correlation.
To predict the gas prices in 2020, you can use the equation you derived from the regression analysis. Simply substitute the year 2020 into the equation, and it will give you an estimated gas price. However, keep in mind that predicting future gas prices is subject to various factors such as economic, political, and environmental influences, which may not be accurately captured in historical data.