Your teacher will give you a piece of pasta and a straightedge.

1. Here are two copies of the same scatter plot. Experiment with drawing lines to fit the data. Draw the line that you think best fits the data. Compare it with a partner’s.

   

   A scatterplot of 20 data values. The horizontal axis has the numbers 0 through 12, in increments of 3, indicated. The vertical axis has the numbers 0 through 40, in increments of 10, indicated. The graph shows the trend of the 20 data points moving linearly downward and to the right. The approximate coordinates of the points are as follows: 1 comma 38. 1 point 5 comma 35. 2 point 3 comma 33. 2 point 5 comma 31 point 5. 3 point 2 comma 32. 4 comma 31. 4 point 4 comma 27. 4 point 5 comma 25. 5 point 8 comma 26. 6 comma 26. 6 comma 22. 6 point 3 comma 18. 7 point 5 comma 14. 7 point 6 comma 21. 8 point 5 comma 17. 9 comma 14. 9 point 3 comma 8. 9 point 5 comma 12. 10 point 4 comma 4. 10 point 5 comma 7.

   

   A scatterplot of 20 data values. The horizontal axis has the numbers 0 through 12, in increments of 3, indicated. The vertical axis has the numbers 0 through 40, in increments of 10, indicated. The graph shows the trend of the 20 data points moving linearly downward and to the right. The approximate coordinates of the points are as follows: 1 comma 38. 1 point 5 comma 35. 2 point 3 comma 33. 2 point 5 comma 31 point 5. 3 point 2 comma 32. 4 comma 31. 4 point 4 comma 27. 4 point 5 comma 25. 5 point 8 comma 26. 6 comma 26. 6 comma 22. 6 point 3 comma 18. 7 point 5 comma 14. 7 point 6 comma 21. 8 point 5 comma 17. 9 comma 14. 9 point 3 comma 8. 9 point 5 comma 12. 10 point 4 comma 4. 10 point 5 comma 7.

2. Here are two copies of another scatter plot. Experiment with drawing lines to fit the data. Draw the line that you think best fits the data. Compare it with a partner’s.

   

   A scatterplot of 20 data points. The horizontal axis has the numbers 0 through 12, in increments of 3, indicated. The vertical axis has the numbers 0 through 40, in increments of 10, indicated. The graph shows the trend of the 20 data points moving linearly upward and to the right. The approximate coordinates of the points are as follows: 1 point 5 comma 1. 2 comma 5. 3 comma 1. 3 comma 7. 3 comma 8. 4 comma 4. 4 point 4 comma 7.5. 4 point 6 comma 10. 5 comma 2. 5 point 5 comma 13. 6 point 2 comma 22. 7 point 4 comma 18. 7 point 5 comma 11. 7 point 5 comma 9. 8 point 8 comma 29. 8 point 9 comma 13. 9 point 1 comma 33. 9 point 7 comma 28. 10 comma 16. 10 comma 17.

   

   A scatterplot of 20 data points. The horizontal axis has the numbers 0 through 12, in increments of 3, indicated. The vertical axis has the numbers 0 through 40, in increments of 10, indicated. The graph shows the trend of the 20 data points moving linearly upward and to the right. The approximate coordinates of the points are as follows: 1 point 5 comma 1. 2 comma 5. 3 comma 1. 3 comma 7. 3 comma 8. 4 comma 4. 4 point 4 comma 7.5. 4 point 6 comma 10. 5 comma 2. 5 point 5 comma 13. 6 point 2 comma 22. 7 point 4 comma 18. 7 point 5 comma 11. 7 point 5 comma 9. 8 point 8 comma 29. 8 point 9 comma 13. 9 point 1 comma 33. 9 point 7 comma 28. 10 comma 16. 10 comma 17.

3. In your own words, describe what makes a line fit a data set well.

The scatter plots both show the year and price for the same 13 used cars. However, each scatter plot shows a different model for the relationship between year and price.

 Scatterplot, horizontal labeled by year, 2 thousand 6 to 2 thousand 16, by 2's. Vertical labeled by price, 6 thousand to 21 thousand, by 3 thousands. A line from two thousand seven comma nine thousand to two thousand fifteen comma seventeen thousand in an upward direction to the right. Contains points two thousand seven comma seven thousand five hundred, two thousand twelve comma fifteen thousand. 

Scatterplot, horizontal labeled by year, 2 thousand 6 to 2 thousand 16, by 2's. Vertical labeled by price, 6 thousand to 21 thousand, by 3 thousands. A line from two thousand seven comma twelve thousand five hundred to two thousand fifteen comma nineteen thousand in an upward direction to the right. Contains points two thousand seven comma twelve thousand and two thousand fourteen comma seventeen thousand.

1. Look at Diagram A.

   1. For how many cars does the model in Diagram A make a good prediction of its price?

   2. For how many cars does the model underestimate the price?

   3. For how many cars does it overestimate the price?

2. Look at Diagram B.

   1. For how many cars does the model in Diagram B make a good prediction of its price?

   2. For how many cars does the model underestimate the price?

   3. For how many cars does it overestimate the price?

3. For how many cars does the prediction made by the model in Diagram A differ by more than \$3,000? What about the model in Diagram B?

4. Which model does a better job of predicting the price of a used car from its year?

1. Is this line a good fit for the data? Explain your reasoning.

   

2. Draw a line that fits the data better.

   

3. Is this line a good fit for the data? Explain your reasoning.

   

   A scatterplot. Horizontal, from 0 to 100 by 25’s. Vertical, from 0 to 200, by 50’s. 20 data points, clustered in two groups of 10. Line drawn, left cluster above line, right cluster below line. Line trends upward and right.

4. Draw a line that fits the data better.