## Lesson 1 Homework Practice Scatter Plots

## Presentation on theme: "Homework Page 11."— Presentation transcript:

1 HomeworkPage 11

2 Lesson 6.6 : Scatter Plots

3 Scatter PlotScatter Plot: A scatter plot is a data display which shows if two sets of data or variables are related- also known as correlation.The graph looks like a bunch of dots, but some of the graphs are a general shape or move in a general direction.

4 Positive CorrelationIf the x-coordinates and the y- coordinates both increase, then it is POSITIVE CORRELATION.This means that both are going up, and they are related.

5 **Positive Correlation Ages and height**

If you look at the age of a child and the child’s height, you will find that as the child gets older, the child gets taller. Because both are going up, it is positive correlation.Age12345678Height “2531343640414755

6 Negative CorrelationIf the x-coordinates and the y- coordinates have one increasing and one decreasing, then it is NEGATIVE CORRELATION.This means that 1 is going up and 1 is going down, making a downhill graph. This means the two are related as opposites.

7 **Negative Correlation Age of car and value of car**

If you look at the age of your family’s car and its value, you will find as the car gets older, the car is worth less. This is negative correlation.Age of car12345Value$30,000$27,000$23,500$18,700$15,350

8 No CorrelationIf there seems to be no pattern, and the points looked scattered, then it is no correlation.This means the two are not related.

9 **No Correlation Shoe size and battering average**

If you look at the size shoe a baseball player wears, and their batting average, you will find that the shoe size does not make the player better or worse, then are not related.

10 **There are three ways to describe data displayed in a scatter plot.**

Positive CorrelationNegative CorrelationNo CorrelationThe values in both data sets increase at the same time-x and y.The values in one data set increase (x) as the values in the other set decrease (y).The values in both data sets show no pattern- scattered.

11 **Which scatterplots below show a linear trend?**

NegativeCorrelationPositiveCorrelationb)d)f)ConstantCorrelation

12 **1. Height and number of vacation days**

What would the scatter plot look like based on the variables below?What type of correlation would it be?1. Height and number of vacation daysThe number of vacation days is not related to height. So there would not be any correlation between these two variables.

13 **There would not be any correlation between these two variables.**

What would the scatter plot look like based on the variables below?What type of correlation would it be?2. Eye color and ageThere would not be any correlation between these two variables.

14 **negative correlation; as age increases, attendance decreases.**

Ticket Out the DoorWrite positive, negative, or no correlation to describe this relationship. Explainnegative correlation; as age increases, attendance decreases.

15 Discuss if the scatter plot shown has a positive correlation, negative correlation, or no correlation. Explain.The graph shows that as the year increases, number of tornados increases. So the graph shows a positive correlation between the data sets.

16 Discuss if the scatter plot shown has a positive correlation, negative correlation, or no correlation. Explain.The graph shows that as area increases, population increases. So the graph shows a positive correlation between the data sets.

17 **Objective - To plot data points in the coordinate plane and interpret scatter plots.**

ySport Utility Vehicles(SUVs) Sales in U.S.54321YearSales (in Millions)19910.919921.1Vehicle Sales (Millions)19931.419941.619951.719962.119972.419982.7x19993.2Year

18 **Scatterplot - a coordinate graph of data points.**

yTrend appears linear.54321Trend is increasing.Vehicle Sales (Millions)Positive correlation.Predict the sales in 2001.xYear

19 **Plot the data on the graph such that homework time **

is on the y-axis and TV time is on the x-axis..Time SpentWatching TVTime Spenton HomeworkStudentSam30 min.180 min.Jon45 min.150 min.Lara120 min.90 min.Darren240 min.30 min.Megan90 min.90 min.Pia150 min.90 min.Crystal180 min.90 min.

20 **Plot the data on the graph such that homework time **

is on the y-axis and TV time is on the x-axis.TVHomework24021018015012090603030 min.180 min.45 min.150 min.120 min.90 min.HomeworkTime on240 min.30 min.90 min.120 min.150 min.120 min.180 min.90 min.Time Watching TV

21 **Describe the relationship between time spent on **

homework and time spent watching TV.Trend appears linear.240210180150120906030Trend is decreasing.HomeworkTime onNegative correlation.Time Watching TV

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?

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