Getting Started 
Misconception/Error The student does not understand how to locate a line of good fit. 
Examples of Student Work at this Level Rather than locating the line to minimize the distances between the line and the data points, the student:
 Draws a line above or belowÂ most of the data points.
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 Draws a curve rather than a line.
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Questions Eliciting Thinking Why did you draw the line where you did?
How well does your line fit the data points?
What makes a line a good fit for data? 
Instructional Implications Explain to the student that the line of fit models the pattern in the data. If the scatterplot is roughly linear, then it is justifiable to model the relationship between the variables with a line. Explain that there are mathematical techniques for locating the line so that the distance between the data points and the line is minimized. When informally fitting a line to the data, the objective is to place the line as close to as many data points as possible. Guide the student to redraw the line so that it better fits the data. Show the student several scatterplots (e.g., ones with a strong positive, strong negative, weak positive, weak negative, and no linear relationship) and model a line of good fit. Explain to the student why the line is (or is not) a good fit for the data. Provide another set of scatterplots and encourage the student to draw a line that fits the data. Assist the student in assessing how well his or her lines fit the data.
Consider implementing the MFAS task Line of Good Fit  2. 
Making Progress 
Misconception/Error The student does not understand how to assess a line of fit. 
Examples of Student Work at this Level The student draws a line of good fit, but does not understand what it means to assess the fit of the line. Rather than assessing the line in terms of its closeness to the data points, the student:
 Says, â€śThe line fits very well.â€ť
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 Describes the relationship between the two variables.
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 Assesses the strength of the correlation between the two variables.
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 Says the line is a good fit because there are equal numbers of points above and below the line or the line is in the middle of the points.
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Questions Eliciting Thinking What does it mean for a line to fit the data?
How can you tell if the line fits the data?
Is it necessary that there be the same number of points above and below the line? 
Instructional Implications Explain how to assess the fit of a line that models data in a scatterplot. Describe the two reasons a line might not fit data the data does not have a linear relationship or the line is not close to the data points. Have the student consider whether the scatterplot suggests a linear pattern and which line is close to as many data points as possible. Guide the student to assess how well a line fits data by addressing how close the line is to the data points.
Provide the student with two small scatterplots (6 â€“ 8 data points) with lines of best fit drawn: one that displays a strong linear relationship and one that displays a weak linear relationship. Ask the student to draw a vertical line segment from each data point to the line of fit. Then have the student measure the line segments and sum their lengths. Explain that the line segments represent each data pointâ€™s distance from the line of fit, so a smaller sum indicates a better fit.
If needed, explain that it is not necessary that there be equal numbers of points above and below the line. Using graphing technology, calculate the line of best fit for the data set {(1, 1), (2, 2), (3, 4), (4, 4)}. Then graph both the points and the line of best fit and show the student that three of the points are below the line while only one point is above.
Consider implementing the MFAS tasks Two Scatterplots and Three Scatterplots. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student draws a line of good fit and assesses the line in terms of how close the data points are to the line. The student says the distance between the line and the data points is minimized or the line is as close to as many of the data points as possible. 
Questions Eliciting Thinking What would your line predict the weight of a sixweek old to be?
Suppose an infant weighed 4 kg. How old is this infant according to your model? 
Instructional Implications Have the student interpret the slope and the yintercept of the line of fit in the context of the data.
Explain how to calculate a data pointâ€™s residual (e.g., the difference between the actual and predicted yvalue). Explain that the leastsquares line of best fit is located so that the sum of the squares of the residuals is minimized. Give the student a small set of data that is roughly linearly related [e.g., (1, 5), (1, 6), (2, 6), (3, 7), (3, 8), (3, 8), (4, 9), (4, 10), (5, 10)]. Ask the student to construct a scatterplot, draw a line that fits the data, and write the equation of the line. Then have the student use the equation to calculate the predicted value of each data point along with its residual. Finally, have the student square and sum the residuals. Allow Got It students to compare their sums to determine whose line best fits the data (the smaller the sum of the squared residuals, the better the fit of the line).
Consider implementing the MFAS task Tuition. 