1. Scatter Plots and Lines of best fit

2. Scatter Plots and Line of Best Fit
Scatter plots =show relationships between two sets of data.
Correlation = describes the type of relationship between two data sets.
Line of Best Fit = is the line that best approximates the linear relationship between two data sets (comes closest to all of the dots on the graph)

3. Correlation Strong Correlation= if the dots are close to the line
Weak Correlation= if the lines are further from the line
Positive Correlation / “Trend”= both data sets increase together (an increasing graph)
Negative Correlation / “Trend”= as one data set increases, the other decreases (a decreasing graph)
No correlation
Positive Correlation
Negative Correlation

4. Patterns in scatter plots
Scatter Plots show Linear Associations when the points cluster along a straight line.
Linear Association
Linear Association

5. Patterns in scatter plots
Scatter Plots show Non-Linear Associations when the points do not cluster along a straight line
Non- Linear Association
Non- Linear Association

6. Patterns in scatter plots
A cluster is where data seems to be gathered around a particular value.
What about this point?
Graph from Learnzillion.com

7. Patterns in scatter plots
Outliers are values much greater or much less than the others in a data set. They lay outside the cluster of correlation
Scatter plots do not always contain outliers.
Do you notice any outliers in these scatter plots?

8. Finding the Line of BEST Fit
Usually there is no single line that passes through all the data points, so you try to find the line that best fits / represents most data.
Step 1: using a ruler, place it on the graph to find where the edge of the ruler touches the most points.
Step 2: Draw in the line. Make sure it touches at least 2 points (best if they are far apart) and try to have approximately half of the data points above the line and half below. Goal is to “center” the line in the data points

9. Finding the Line of BEST Fit
Step 3: Calculate the slope between two points on your line (best if they are far apart)
Step 4: Calculate the y intercept by substituting the slope and one point on the line into slope-intercept form of an equation and solve for “b.”
Step 5: Write the equation of the line in slope-intercept form.

10. Practice Problem… The Olympic Games Discus Throw
Year Winning throw
The Olympic games discus throws from 1908 to 1996 are shown on the table.
Approximate the best - fitting line for these throws let x represent the year with x = 8 corresponding to Let y represent the winning throw.
View scatter plot on handout.

11. Step 1 & 2: Place your ruler on the page and draw a line where it touches the most points on the graph.

12. Step 3: Find the slope between 2 points on the line.
The line went right through the point at 1960 and 1988.
The ordered pairs for these points are (60, 194.2) and (88, 225.8).
m = y2 – y1 = – = = 32 = x2 – x –
m =

13. Step 4: Find the y-intercept.
Substitute the slope and one point into the slope-intercept form of an equation.
Slope: 8/7 and a point: (88, 225.8)
y = mx + b = 8/7(88) + b
225.8 = 704/7 + b
225.8 = ≈ b
125.2 = b

14. Step 5: Write in slope-intercept form.
Substitute each value into y = mx + b.
The equation of the line of best fit is:
y = 8/7 x
When you solve these problems, you can get different answers for the line of best fit if you choose different points. But the equations should be close.

15. 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.

16. -33 38 Draw the line of best fit. Find the slope. (20, 67) & (58, 34)
34 – 67 = 58 – 20
Plug into y = mx + b
67 = -33/38(20) + b
Solve for b
67 = b
b = 84.7
Write in slope-intercept form
y = -33/38x
-33 38
Is this a strong or weak correlation?
Does that make it easier or harder to place the line of best fit?

17. Ticket Prices and Sales
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?

18. 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)

19. 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 8

20. 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 = -5/8x + 10

21. History Vs. Math
Here is a scatter plot showing the relationship between students who took a History Test and a Math Test.
Is there a relationship between the scores?
Describe the relationship.

22. History Vs. Math
Since there is a positive correlation with the data, predict what a student who earned a 75% on their history test earned on their math test.
What can I draw that will help me make that prediction?

23. History Vs. Math
75% on History Test
The line of best fit will help you make a prediction as to what score the student would get on their math test if they earned a 75% on their history test.
What score would he get on the math test?
About 77%

24. Population of Goldfish & Star fish
The following table shows the population between goldfish and star fish at different aquariums.
Goldfish 13 18 19 20 27 16 22 24 32 12
Star Fish 30 25 15 28 10 29
Is there a relationship in this data?
What can we draw to see if there is a relationship?
Draw a scatter plot 

25. Goldfish & Star Fish Is there a relationship with this data?
What kind of relationship is it?
If I have a goldfish population of 15, how many star fish will there be?
What can I draw to help me make that prediction?

26. Goldfish & Star Fish Draw a line of best fit.
If I have a goldfish population of 15, how many star fish will there be?
There would be about 26 star fish.