______________________
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Activity:Line
of Best Fit
Consider
the following data, where
Row is the row number where the student sits in class, and
Grade is the student’s grade in the course, using the usual 4 point scale.
Row Grade
1
4
2
2
4
3
6
0
7
1
Several
attempts have been made to draw a line through the data.See
below.
1.Which
is the “best fitting” line, in your opinion? _____
2.Which
is the “worst fitting” line, in your opinion? _____
3.Give
a general statement summarizing why you made these choices.
4. Try
to come up with a way to quantify your reasoning in #3. Can
you come up with some objective way to measure how well a line fits (or
how poorly it fits)?
Attempt
A
Attempt
B
Attempt
C
Follow-up:
For
each attempted line, find the vertical distances from each data point to
the line. These are called
“errors” or “residuals”.
Attempt
A
Row Grade
Error
1
4
2
2
4
3
6
0
7
1
Attempt
B
Row Grade
Error
1
4
2
2
4
3
6
0
7
1
Attempt
C
Row Grade Error
1
4
2
2
4
3
6
0
7
1
5. Which
line has errors which tend to be smallest in magnitude?____
6. Which
line has errors which tend to be largest in magnitude?____
7. What
single quantity would you use to summarize the set of errors for any attempted
line? (This quantity should
serve as a criterion for deciding on the “best-fitting” line.)
8. Compute
this quantity for each of the three attempts.
Attempt A ______ Attempt
B ______
Attempt C ______
9. Now use these quantities to rate the 3 attempts. Which attempted line was best ____ and which was worst ____ using your criterion? Do these choices square with your earlier answers – Q1 & Q2 ?