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Scatter Plots Find the line of best fit.

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43210 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas. The student will construct, interpret and identify patterns of associations for bivariate data displayed in two- way tables and scatterplots. - Write equation of line-of-best-fit. And use it to make predictions. - Calculate relative frequencies and describe their meaning. The student will construct scatterplots and two-way tables from bivariate data. - Draw line-of- best-fit for scatter plot. - Identify patterns of associations. - Able to generally describe relationship of bivariate data displayed in a two-way table. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with investigating patterns of association with bivariate data. Focus 7 - Learning Goal #2: The student will construct, interpret and identify patterns of associations for bivariate data displayed in two-way tables and scatterplots.

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Line of Best Fit Scatter plots show relationships between two sets of data. If there is a relationship between the two sets of data, we need to draw in a “Line of Best Fit” This is a line that is the line that comes closes to all of the dots on the graph. However, it does not touch all of the dots. If the dots are close to the line, the graph has a strong correlation. If the lines are further from the line, the graph has a weak correlation.

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Create a Scatter Plot Use the data on the price per ticket and how many tickets were sold to create a scatter plot.

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This is a scatter plot for ticket sales for a school play. This shows the relationship between ticket price and how many tickets were sold. Place a ruler on the graph. Try to get it to touch as many points as possible. Try to have an equal number of points above and below the line. Then draw a line. This is the “Line of Best Fit” for this graph. Is this a strong or weak correlation?

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Write the equation of the line of best fit. What information do we need in order to write an equation of a line? y = mx + b We need a slope and a y intercept. How do find the y-intercept? Where does your line cross the y-axis? About (0, 10)

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Write the equation of the line of best fit. How do we find slope? Pick two points that touch the line that are far apart. The ordered pairs are listed in your table of data. (2, 8) & (10, 3) 3 – 8 = 10 - 2 -5 8

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Write the equation of the line of best fit. We have a y-intercept (0, 10). We have a slope of - 5 / 8. We can substitute that information into the equation y = mx + b. Remember m is the slope and b is the y-intercept. The equation of the line of best fit is: y = - 5 / 8 x + 10

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Try it again… The circus performs 10 times. Each time they keep data on the number of water bottles and lunch boxes sold. Use the data provided to make a scatter plot. Draw the line of best fit. Write the equation of the line of best fit.

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Write equation of line of best fit. Draw the line of best fit. Find the y-intercept. About (0, 85) Find the slope. (20, 67) & (58, 34) 34 – 67 = 58 – 20 y = mx + b y = - 33 / 38 x + 85 -33 38 Is this a strong or weak correlation?

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