Scatter Plots Find the line of best fit

Scatter Plots Find the line of best fit.

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. 4 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. 3 The student will construct, interpret and identify patterns of associations for bivariate data displayed in twoway tables and scatterplots. - Write equation of line-of-best-fit. And use it to make predictions. - Calculate relative frequencies and describe their meaning. 2 The student will construct scatterplots and two-way tables from bivariate data. - Draw line-ofbest-fit for scatter plot. - Identify patterns of associations. - Able to generally describe relationship of bivariate data displayed in a two -way table. 1 With help from the teacher, the student has partial success with level 2 and 3 elements. 0 Even with help, students have no success with investigating patterns of association with bivariate data.

• 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. Line of Best Fit

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

Ticket Price and Sales Number of Tickets Sold • 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. 9 8 7 6 5 4 3 2 1 0 0 5 10 Cost Per Ticket 15 Is this a strong or weak correlation?

• 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) 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 = -5 10 - 2 8 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 Write the equation of the line of best fit.

• 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. Try it again…

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