Getting Started 
Misconception/Error The student does not understand how to assess a line of good fit. 
Examples of Student Work at this Level Rather than assessing how well each line fits its set of data, the student:
 Makes an observation about the scatterplots that does not address the degree of fit of the lines.
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 Attempts to apply the vertical line test to the data points.
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 Makes an unclear statement.
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 Connects the data points in some order and compares the number of times the lines of fit are intersected.
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Questions Eliciting Thinking What is a scatterplot?
Imagine if the lines had not been drawn. Do you see any pattern in the data?
What makes a line of good fit for a set of data? 
Instructional Implications Review the concept of twovariable or bivariate data with the student and provide examples of both onevariable (e.g., the heights of the students at the school) and twovariable data (e.g., the ages and heights of the students at the school). Explain that the scatterplot is a visual representation of twovariable data and that a 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. Ask the student which line tends to be closer to its data points. Emphasize that not all data is linear or displays a pattern that can be easily described. However, both of these sets of data show a generally linear pattern. Nonetheless, the first set shows a strong positive linear pattern while the second set of data shows a weaker positive linear pattern. Consequently, the line in the first graph fits its data better than the line in the second graph.
Provide opportunities to construct scatterplots, draw a line that fits the data, and assess the degree of fit.
Consider implementing the MFAS tasks Line of Good Fit 1Â or Line of Good Fit 2. 
Moving Forward 
Misconception/Error The student does not compare the fit of the lines. 
Examples of Student Work at this Level The student appears to understand how to assess the fit of a line to a set of data but does not directly compare the fit of the lines.
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Questions Eliciting Thinking What makes a line a good fit for a set of data?
Does one of the lines fit its data better? Why or why not? 
Instructional Implications Guide the student to compare how well the lines fit their sets of data. Remind the student that a line is a good fit for a set of data if the distances between the data points and the line are small. Explain 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. Ask the student if each set of points is generally linear and then ask the student to compare how close each line is to its 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.
Consider implementing the MFAS task Three Scatterplots. 
Almost There 
Misconception/Error The student uses incorrect or imprecise terminology. 
Examples of Student Work at this Level The student compares the fit of the lines to the data they model but uses incorrect or imprecise terminology. The student:
 Refers to the data points as â€śdotsâ€ť and discusses the placement of the data points around the line rather than fitting the line to the data.
 Describes the data in the second plot as â€śgoing everywhere.â€ť

Questions Eliciting Thinking What mathematical term can you use to describe the dots?
Is the data fitted to the line or the line fitted to the data?
Can you be a little more precise in describing the second plot? 
Instructional Implications Review terms used to describe scatterplots and linear relationships, for example, positive linear, negative linear, data points, scatter, clusters, outliers, patterns, and deviations. Guide the student to assess and compare scatterplots in terms of their form, direction, and strength. Model comparing the two scatterplots using appropriate terminology. Provide a number of scatterplots displaying various types of associations and ask the student to describe the relationship between the variables. 
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 says that the line in the first graph fits the data better because the data points are either on the line or very close to it. The student explains that although the data in the second graph is roughly linear, the line does not fit the data as well because the data points are more widely scattered about the line. 
Questions Eliciting Thinking Is there a better way to model the second set of data? Could the line be placed differently or a different type of function used?
Suppose an exponential function is used to model data in a scatterplot. What might that scatterplot look like? 
Instructional Implications Introduce the student to the correlation coefficient, r, and explain it as a measure of the degree of linear relationship. Guide the student to develop an understanding of the correlation coefficient by showing the student a number of scatterplots and their associated r values.
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, 9), (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. 