Question
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
Can this data set be best modeled with a linear function, a quadratic function, or an exponential function? Explain. already done.
Raimy asked 10 people how far they drove and how much gas they used. When we look at the numbers, it seems like the more miles people drove, the more gas they needed, but not in a simple straight line. Instead, it looks like the amount of gas goes up faster as the miles increase, which suggests it's not a straight line (linear) or a curve that opens up or down (quadratic). It looks more like an exponential function because the gas usage gets bigger quickly with the longer miles.
Use technology to create an appropriate regression model. Explain the steps you took and your result. already done.
I used a computer program to find out what kind of math equation fits Raimy's data best. First, I put all the miles and gas numbers into the program. Then, I asked it to try different kinds of equations: a straight line, a curve that goes up and down, and a curve that goes up really quickly. The program showed that the curve that goes up quickly (like an exponential function) matched the data the best. In the end, I found an equation that helps predict how much gas people will use based on how many miles they drove.
Use your scatter plot and regression model to interpret the data set in terms of the given context. What conclusions can you draw from this data set? already done.
I made a scatter plot with Raimy's data that shows how many miles people drove and how much gas they used. When I looked at the dots on the plot, I saw that as the miles went up, the gas usage went up really fast too. Using my computer program, I found an equation that fits this data well and looks like an exponential curve. This means the more miles people drive, the more gas they need, and it increases quickly. So, if someone drives a lot, they will use a lot of gas! This helps us understand that driving longer distances means needing way more gas than just a little bit.
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.
make it simple in a small paragraph and like a kid wrote it.
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
Can this data set be best modeled with a linear function, a quadratic function, or an exponential function? Explain. already done.
Raimy asked 10 people how far they drove and how much gas they used. When we look at the numbers, it seems like the more miles people drove, the more gas they needed, but not in a simple straight line. Instead, it looks like the amount of gas goes up faster as the miles increase, which suggests it's not a straight line (linear) or a curve that opens up or down (quadratic). It looks more like an exponential function because the gas usage gets bigger quickly with the longer miles.
Use technology to create an appropriate regression model. Explain the steps you took and your result. already done.
I used a computer program to find out what kind of math equation fits Raimy's data best. First, I put all the miles and gas numbers into the program. Then, I asked it to try different kinds of equations: a straight line, a curve that goes up and down, and a curve that goes up really quickly. The program showed that the curve that goes up quickly (like an exponential function) matched the data the best. In the end, I found an equation that helps predict how much gas people will use based on how many miles they drove.
Use your scatter plot and regression model to interpret the data set in terms of the given context. What conclusions can you draw from this data set? already done.
I made a scatter plot with Raimy's data that shows how many miles people drove and how much gas they used. When I looked at the dots on the plot, I saw that as the miles went up, the gas usage went up really fast too. Using my computer program, I found an equation that fits this data well and looks like an exponential curve. This means the more miles people drive, the more gas they need, and it increases quickly. So, if someone drives a lot, they will use a lot of gas! This helps us understand that driving longer distances means needing way more gas than just a little bit.
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.
make it simple in a small paragraph and like a kid wrote it.
Answers
GPT-4o mini
**Question:** If Raimy's regression model shows that for every extra 100 miles driven, a person uses about 2 gallons more of gas, what does that tell you about how much gas people need when they drive longer distances?
**Answer:** This means that as people drive more miles, they need even more gas! For every 100 miles they drive, they are using about 2 extra gallons of gas. So, if someone drives a lot, they're going to need a lot more gas compared to just driving a little bit. It shows us that driving far distances really makes gas usage go up a lot!
**Answer:** This means that as people drive more miles, they need even more gas! For every 100 miles they drive, they are using about 2 extra gallons of gas. So, if someone drives a lot, they're going to need a lot more gas compared to just driving a little bit. It shows us that driving far distances really makes gas usage go up a lot!