Scatter plots 04:40 minutes

Video Transcript

Transcript Scatter plots

Poor Billy Fakespeare the Ghost - his Medieval Party was a bust. Hardly any ghost guest showed. But, to celebrate his 400th birthday, he’s determined to have a big Luau themed shindig with lots and lots of guests. To plan the perfect party, he uses scatter plots.

Postive correlations

On a Cartesian plane, scatter plots are used to show the relation between variables to identify trends. Take a look at this scatter plot – it shows the relation of the popularity of a DJ to the number of guests attending a party. For example, a DJ with a 50 percent popularity rating had 200 guests in attendance and a DJ with a popularity rating of 80 percent had 350 guests. The graph indicates a trend: The more popular the DJ, the greater the attendance at the party. Notice the points on the graph are grouped together - this indicates a high correlation.

And since both variables increase together, the correlation is positive. When points are grouped together, you can draw a 'trend line' also known as the 'line of best fit'and by using any two points that lie on or near the line, you can calculate the slope of the line. And then use the slope and one of the known points to write an equation for the trend line. For this line, using slope equal to 5 and the ordered pair 50 and 200, we can figure out the equation of the line. You can also use the trend line to predict unknown values for 'x' and 'y'. For 'x' equal to 20, we can determine that 'y' is equal to 50 is a better prediction than 'y' is equal to 300.

Negative correlations

Fakespeare thinks he’s got the entertainment for the party all figured out. He invites DJ Mozart to rock the house, but he wonders, is music enough? What about games? He does some research. Take a look at the table. Is there a trend between the number of silly party games and party attendance? Let’s design a scatter plot. For the x-axis, list the number of games, and for the y-axis, list the attendance. Now, plot the order pairs. Hmmm, the points are grouped together, so the data is highly correlated, but as the number of games increases, the number of guests decreases and this indicates a negative correlation.

When there is a negative correlation, as one variable increases, the other decreases. You don’t need to be a genius to figure out that party games are a terrible idea, so Fakespeare decides, there will be no party games. What about refreshments? Will having tropical drink umbrellas make people want to come to the party? Let’s take a look at the scatter plot and see if there's a trend. The points on the graph are very spread out, so there is no correlation and no trend. Tropical drink umbrellas might not increase attendance, but they won’t have an adverse effect either, so Fakespeare orders a case just because he likes them. It seems as though Fakespeare has got everything under control, but do you? Let’s make sure you are good to go with scatter plots.

Correlation Interpretation

When the data is spread out with no pattern, that means there is little to no correlation and no trend. Althought this scatter plot shows the points grouped together, there is no trend. If the line of best fit is horizontal that means that what we measure on the x-axis has no influence on what we're measuring on the y-axis. What if the line of best fit is vertical? Since the slope of a vertical line is undefined, there is no correlation and no trend. One last note: If there is a correlation, don’t automatically jump to the conclusion that there is also a trend. You will need to use common sense because sometimes a correlation is not causation – meaning, one thing does not necessarily cause the other. Take a look at this example. Based on the trend line you might think the house number and party attendance are related, but that’s coincidence, not a trend. When interpreting trends, remember to use common sense. Fakespeare’s party is a huge success! Too bad though. none of the photos that were snapped lasted very long, maybe they're on to something?