Scatter Plots and Lines of Best Fit
Scatter Plot – a graph that consists of a set of points, showing the relationship between two variables
To create a scatter plot:
· Determine the independent and dependent variables. The independent variable is on the horizontal (X) axis, the dependent variable is on the vertical (Y) axis – just like all other graphs!
· Label the axes (including units) and give the graph a title.
· Scale the axes
o Think about your maximum and minimum values before deciding on the scale.
o Also read the questions below to see how far you need to extend your axes (max/min).
Example: The daily attendance at a local swimming pool was compared to the highest daily temperature:
Temperature (°C) / 28 / 33 / 31 / 26 / 24 / 22 / 18 / 21 / 20Number of people / 191 / 212 / 219 / 188 / 183 / 176 / 163 / 180 / 172
Line of Best Fit – a line used in scatter plots to show a trend within the data
To draw a line of best fit:
· Draw a straight line through or close to as many points as possible (Use a ruler!)
· TRY to have the same number of points above and below the line.
· The line does not have to go through (0, 0).
DRAW IN A LINE OF BEST FIT ON YOUR SCATTER PLOT.
Why do we use lines of best fit? TO MAKE PREDICTIONS!
· Scientists use lines of best fit when they make graphs using their observations. This allows them to predict what will happen in cases they did not test.
There are two types of predictions:
· Interpolation: make a prediction that falls inside the range of data
· Extrapolation: make a prediction that falls outside the range of data (extend your line)
How accurate are my predictions?
· The more closely the line fits the data, the more confident one can be in making predictions.
· If the data points all fall fairly close to the line of best fit, then you can be fairly confident making predictions using the best-fit line.
· If the data are scattered far from the line of best-fit, predictions may not be reliable.
For the above example:
a) Predict the temperature on a day when there were 200 people at the pool. ______
Is this interpolation or extrapolation? ______
b) Predict the number of people at the pool on a day when the temperature was 34°C. ______
Is this interpolation or extrapolation? ______
c) How good do you think your predictions are? Explain.
Find a Summer Holiday Friend Activity (Matchmaker)
Without consulting with any other students, please rank the following summer activities from 1 to 10, with 1 meaning you’d like to do that activity the most, and 10 meaning you’d like to do that activity the least.
My Rank (x) / Activity / Friend’s Rank (y) / Ordered Pairs (x, y)Go to the beach
Go to the fair
See a movie at the theatre
Go for a swim at the pool
Go camping
Go shopping at the mall
Read a book
Play organized sports (basketball/soccer/etc.)
Go to a music concert
Play video games
Find a friend and copy down their activity rankings. Number and label the axes, and plot the ordered pairs below.
Part 2: Find someone in the class who has very similar likes to you in terms of these activities OR completely opposite likes to you. Complete the table of values below and graph your coordinates (your x coordinates are just the same as the ones in part 1).
My Rank(x) / Activity / Friend’s Rank (y) / Ordered Pairs (x, y)
Go to the beach
Go to the fair
See a movie at the theatre
Go for a swim at the pool
Go camping
Go shopping at the mall
Read a book
Play organized sports (basketball/soccer/etc.)
Go to a music concert
Play video games
Graph (label the same as you did before).
How does your graph look? Did your prediction from question 2 or 3 on page 1 come true? Explain.
Correlation = relationship
r is called the correlation coefficient; it is a measure of how well the line ‘fits’ the data.
A ‘perfect fit’ means that all points lie on the line. The closer r is to 1 or -1, the closer the line fits the data. A low r value indicates that the line does not fit the data well, and would thus you would not be able to make accurate predictions using the equation for the line.
Types of Correlations
r value / Type of correlation / What the graph looks like / How accurate are the predictions? / Exampler = 1
r = 0
r = -1
r = 0.89
r = 0.34
r = -0.999
Using the TI-84 to create a line of best fit:
This table shows the winning times for the women’s 1500-m Olympic speed skating even since 1976.
Correlation coefficient (r)
Ex: In the example above, what is the r value? r = ______
Is this a good line of best fit – can you make accurate predictions from it?
Is it a positive correlation or negative correlation? ______
Problems for you to try:
r = ______r = ______
Description of line of best fit: ______Description of line of best fit: ______
r = ______r = ______
Description of line of best fit: ______Description of line of best fit: ______
2) Which of the following equations is the best fit for the data? How do you know?
Equation with best fit: ______How do you know? ______
3) You used the TI-84 to input a table of values and then performed a linear regression on the data. Use the information on the screen below to answer the following:
a) Write the linear equation for the line of best fit for the data in slope-intercept form (round values to two decimal places). Equation: ______
b) Give the value of the correlation coefficient. r = ______
c) How well does the line fit the data? ______