**Instructional Implications**Explain that the scatterplot is a visual representation of two-variable 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 closest to its data points. Emphasize that not all data is linear or displays a pattern that can be easily described. However, this set of data shows a generally linear pattern. It is the placement of the lines that vary. Guide the student to assess how well a line fits data by addressing how close the line is to the data points.
Provide opportunities to construct scatterplots, draw lines that fit the data, and assess the degree of fit.
Consider implementing the MFAS tasks *Line of Good Fit - 1* or *Line of Good Fit - 2* (8.SP.1.2). |

**Instructional Implications**Review the two reasons a line might not fit data: 1) the data does not have a linear relationship; or 2) the line is not close to the data points. Model a concise explanation using appropriate terminology. Address both the fact that the scatterplot suggests a linear pattern and that the student’s line is close to as many data points as possible.
Provide the student with two small scatterplots (6 – 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 point’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 task *Two Scatterplots* (8.SP.1.2). |

**Instructional Implications**Explain how to calculate a data point’s residual (e.g., the difference between the actual and predicted y-value). Explain that the least-squares 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* (8.SP.1.3). |