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Unit 4: Linear Relations Minds On 1.Determine which variable is dependent and which is independent. 2.Graph the data. 3.Label and title the graph. 4.Is there a relationship? How many km you have driven 0102030405060 How much gas is in your tank (L) 60524436282012

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Learning Goals: Draw a line of best fit and use it to make predictions about a scatter plot Make predictions about the relationship between two variables using interpolation and extrapolation

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit What can you tell me about this graph? It shows a perfect linear trend It is easy to draw a straight line through all the points

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When the points on our scatter plot do not make a perfect straight line, we draw a line of best fit. Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit The line of best fit tries to get as close as possible to every point

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit What can you tell me about this graph? It shows a strong linear trend It is easy to draw a straight line through all the points

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Success Criteria for drawing a line of best fit: The line should pass through as many points as possible There should be an equal number of points above and below the line The line of best fit does not need to pass through the origin Outliers do not need to be included in the line of best fit

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Which line would you use for the line of best fit? Look back at the success criteria for drawing a line of best fit.

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Draw a line of best fit for each of the scatter plots that show a linear relationship below. Write two or three key words to describe each relation on the line below the scatter plot. (rises upward to the right, falls downward to the right, no relationship, strong, weak, linear, non-linear)

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Draw a line of best fit for each of the scatter plots that show a linear relationship below. Write two or three key words to describe each relation on the line below the scatter plot. (rises upward to the right, falls downward to the right, no relationship, strong, weak, linear, non-linear)

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Draw a line of best fit for each of the scatter plots that show a linear relationship below. Write two or three key words to describe each relation on the line below the scatter plot. (rises upward to the right, falls downward to the right, no relationship, strong, weak, linear, non-linear)

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Why do we draw a line of best fit? So we can use it to make predictions for values that were not actually recorded in the table or plotted on the scatter plot. So we can see the relationship between the data.

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit The line of best fit helps us to determine how the two variables are related. Our variables can have strong or weak correlations. Our variables can have a negative or positive correlation.

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit What does a strong correlation look like? What does a weak correlation look like?

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit What does a negative correlation mean? What does a positive correlation mean?

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit How do you know if the correlation is strong or weak? If the points nearly form a line, then the correlation is ___________________. If the points are dispersed more widely, but still form a rough line, then the correlation is _______________________.

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit The line of best fit allows us to make predictions for values that were not actually recorded in the table or plotted on the scatter plot. There are two ways we can do this: 1.Interpolate: Estimating for points within the data 2.Extrapolate: Estimating for points outside the data (finding a value that is before the first point or after the last point)

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Interpolate: Remember Julie? How old was she when she was 100cm tall? Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit

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Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit Extrapolate: How tall will Julie be when she is 9 years old?

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Practice: Pg. 68 Read Key Ideas Pg. 69 (line of best fit) Q. 3ab, 6c, 7, 10, 11 Pg. 74 Read Key Ideas and Example and Solution Pg. 75 (correlation) Q. 1, 4, 5, 8, 11, 12 Pg. 82 Q. 14ab Unit 4: Linear Relations Lesson 3: Scatter Plots and the Line of Best Fit

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7-3 Line of Best Fit Objectives

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