8.SP.A.2: Know that straight lines are widely used to model relationships between two quantitative… — Practice

Work through problems with immediate feedback

Concepts

A scatter plot shows outdoor temperature versus the number of
layers of clothing people are wearing. The points form a clear
downward curve: layers drop sharply as temperature rises from
cold to mild, then level off with little further change as it
gets even warmer. Should a straight line be used to model this
data?

Yes -- a straight line can always summarize any scatter plot, curved or not

No -- the pattern is curved (nonlinear), so a straight line would misrepresent it

Yes, but only if the line is drawn very steep

No -- there is no association between the variables at all

A tutor draws a straight line through a scatter plot of
study-hours versus test scores. The line does not pass through
most of the individual data points. A student says, "That can't
be a good line -- it's not even touching most of the points!"
What is the best response to the student?

The student is right -- a good line should pass through as many data points as possible

The line is a model that summarizes the overall trend; it is not expected to pass through most individual points, only to follow the general pattern and sit in the balance of the data

The line is wrong and should be redrawn to touch more points, even if that makes it less balanced

The line only needs to touch the highest and lowest data points

Two students each draw an informal line of best fit for the same
scatter plot. Their lines are similar in direction and position
but not identical -- one has a slightly steeper slope than the
other. Both lines follow the trend and are reasonably balanced
in the data. What should we conclude?

One of the two lines must be wrong, since there can only be one correct line of best fit

Both lines can be reasonable; informal fitting by eye does not produce one single exact answer

The steeper line is automatically the better one

The shallower line is automatically the better one

Line P has a slope of 5 and the data points are widely scattered
around it. Line Q has a slope of 0.5 and the data points cluster
tightly around it. Which line is a better fit for its data?

Line P, because a steeper slope means a stronger relationship

Line Q, because its data points cluster tightly around the line, regardless of slope

Both are equally good fits, since fit quality is not related to scatter

Neither -- fit quality can only be judged with a formula, not by eye

Applications

A scatter plot of 15 data points shows a positive linear
association. Line A follows the upward trend and has
roughly 7 points above it and 8 below, staying close to the
data throughout. Line B passes exactly through the two
highest data points but leaves 13 of the 15 points below it.
Which line is the better fit, and why?

Line A -- it is balanced (roughly equal points above and below) and stays close to the data overall

Line B -- it passes exactly through two real data points, which makes it more accurate

Both are equally good, since both follow the general upward direction

Neither -- a good fit requires the line to touch every data point

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Fitting Lines to Data -- Tutor Intake Assessment

Concepts

Applications