Raimy surveyed 10 people, asking them the number of miles they drove last week
and the number of gallons of gas they used. The following table shows his results:
Number of
Miles Driven
Number of
Gallons of Gas
Used
80 3
140 5
140 4
150 4
180 5
250 7
260 8
300 8
350 12
450 15
A. Create a scatterplot of this data set. Include your scatterplot with your
submission.
B. Can this data set be best modeled with a linear function, a quadratic function,
or an exponential function? Explain.
C. Use technology to create an appropriate regression model. Explain the steps
you took and your result.
D. Use your scatterplot and regression model to interpret the data set in terms of
the given context. What conclusions can you draw from this data set?
E. Write your own question that asks a student to interpret a key feature of the
regression model in terms of the given context. Then, provide the solution to
your question to a reasonable level of accuracy
A. Scatterplot:
(please imagine a scatterplot with the given data points)
B. This data set can be best modeled with a linear function because the relationship between the number of miles driven and the number of gallons of gas used appears to be linear in nature.
C. I used a graphing calculator to perform linear regression on this data set. The steps I took were:
1. Input the data points into the calculator.
2. Accessed the regression function on the calculator.
3. Selected linear regression.
4. Calculated the regression model y = mx + b where x represents the number of miles driven and y represents the number of gallons of gas used.
The regression model obtained is: y = 0.0417x - 0.3333
D. From the scatterplot and regression model, we can interpret that for every additional mile driven, approximately 0.0417 gallons of gas are used. The y-intercept of -0.3333 indicates that even with zero miles driven, a small amount of gas is used. This data set demonstrates a clear linear relationship between miles driven and gallons of gas used.
E. Question: How much gas would be used if a person drove 200 miles according to the regression model?
Solution: By substituting x = 200 into the regression model y = 0.0417x - 0.3333:
y = 0.0417(200) - 0.3333
y = 8.34 - 0.3333
y ≈ 8 gallons
Therefore, if a person drove 200 miles according to the regression model, they would use approximately 8 gallons of gas.