Transcript 8-1 Blah Blah Blah - Integrated Math 1
Warm Up
On your whiteboards…
Draw a coordinate plane, then graph and label each point.
1. A(3, 2) 3. C(–2, –1) 5. E(1, 0) 2. B(–3, 3) 4. D(0, –3) 6. F(3, –2)
Scatter Plots
SWBAT use scatter plots to determine the strength of relationship between two data sets and distinguish between correlation and causation. 3.1.b.ii
D.O.L. Given 4 CR questions, students will use scatter plots to determine the strength of relationship between two data sets and distinguish between correlation and causation with 75% accuracy.
Why : Scatter plots let us see how one variable can have an impact or relationship on another variable. This relationship also allows us to identify trends and make predictions about relationships.
Essential Question
How do we describe real-life data displayed in graphs?
Think – Pair - Share
Suppose you worked at a video store. The number of videos you sold in a five year period is shown on the graph.
1. Explain the trend you see.
2. Estimate the number of movies sold on video sold in 2003.
Scatter plots
Scatter plot – A graph of plotted points that shows the relationship between two sets of data. • In a scatter plot, the two sets of data are graphed as ordered pairs (x, y) on a coordinate system.
Scatter plots let us the see a correlation in the data, establish trends, and make predictions about future events.
Correlations: How do the data relate?
Correlation – The relationship between two variables As x increase, y _______.
As x increase, y _______.
Say it together…
Describe Correlations from Scatter Plots
Describe the correlation illustrated by the scatter plot. (as x increase, y ________)
As the average daily temperature increased, the number of visitors increased.
There is a positive correlation between the two data sets.
Describe Correlations from Scatter Plots
Describe the correlation illustrated by the scatter plot. (as x increase, y ________)
As the years increased, the number of participants in the snowboarding competition increased.
There is a positive correlation between the two data sets.
Describe Correlations from Two Data Sets
Choose the correct correlation:
the average temperature in a city and the number of speeding tickets given in the city
A) As the temperature increases, the number of speeding tickets increases.
B) As the temperature increases, the number of speeding tickets increases.
C) As the temperature decreases, the number of speeding tickets increases.
D) The number of speeding tickets has nothing to do with the temperature.
Describe Correlations from Two Data Sets
Choose the correct correlation: Ticket sales and the number of people in an audience.
A) As ticket sales increase, the number of people in an audience increases. B) As ticket sales increase, the number of people in an audience decreases.
C) As ticket sales decrease, the number of people in an audience increases.
D) The number of ticket sales has nothing to do with the number of people in an audience.
Your turn!
Explain the correlation you would expect to see between the pair of data sets. a runner’s time and the distance to the finish line
You would expect to see a negative correlation. As a runner’s time increases, the distance to the finish line decreases.
Your turn!
Explain the correlation you would expect to see between the pair of data sets. the number of times you sharpen your pencil and the length of your pencil
You would expect to see a negative correlation. As the number of times you sharpen your pencil increases, the length of your pencil decreases.
Your turn!
Explain the correlation you would expect to see between the pair of data sets. the temperature in Houston and the number of cars sold in Boston
You would expect to see no correlation. The temperature in Houston has nothing to do with the number of cars sold in Boston.
Your turn!
Explain the correlation you would expect to see between the pair of data sets. the number of members in a family and the size of the family’s grocery bill
You would expect to see positive correlation. As the number of members in a family increases, the size of the grocery bill increases.
Correlation vs. Causation
Causal relationship – A relationship in which one thing causes another Causal – When the temperature goes up, the amount of clothes people wear goes down A strong correlation between two data sets doesn’t mean they have a causal relationship
Correlation is not causation!
Correlation is not causation!
Correlation is not causation!
What’s wrong with this logic?
Think-Pair-Share
What’s an example of two things that might have correlation, but not causation?
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.
Graph A Graph B Graph C
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.
Graph A
The age of the car cannot be negative.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.
Graph B
This graph shows all positive values and a positive correlation, so it could represent the data set.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.
Graph C
There will be a positive correlation between the amount spent on repairs and the age of the car.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.
Graph A Graph B Graph C
Graph A shows negative values, so it is incorrect. Graph C shows negative correlation, so it is incorrect. Graph B is the correct scatter plot.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. Graph A Graph B Graph C
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. G raph A
The pie is cooling steadily after it is take from the oven.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. Graph B
The pie has started cooling before it is taken from the oven.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. Graph C
The temperature of the pie is increasing after it is taken from the oven.
Matching Scatter Plots to Situations
Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. Graph A Graph B Graph C
Graph B shows the pie cooling while it is in the oven, so it is incorrect. Graph C shows the temperature of the pie increasing, so it is incorrect. Graph A is the correct answer.
Looking at a table
Explain the correlation:
Time pooper scoopers clean the park vs. number of dogs in the park
Dogs Hours 10 20 2 2.5
30 40 4 5
As the number of dogs in the park increases, the number of hours it takes pooper scoopers to clean the park increases: Positive Correlation
Looking at a table
Explain the correlation:
Number of squirrels in park vs. number of dogs in park
Dogs Squirrels 10 20 200 158 30 40 140 100
As the number of dogs in the park increases, the number squirrels decreases: Negative Correlation
Essential Question
How do we describe real-life data displayed in graphs?
D.O.L.
1A. Explain the correlation illustrated by the scatter plot. 1B. If there’s a correlation, justify whether the data sets might have a causal or non-causal relationship.
There is a positive correlation between the two data sets.
As the number of fat grams increased, the number of calories also increased.
Fat and calories have a causal relationships, because the amount of fat directly impacts the amount of calories in food.
D.O.L.
2A. Explain the correlation illustrated by the scatter plot. 2B. If there’s a correlation, justify whether the data sets might have a causal or non-causal relationship.
There is a negative correlation between the two data sets.
As the weight of the vehicle increased, the gas mileage decreased.
Weight and mpg have a causal relationships, because the weight of a car directly impacts its gas mileage.
D.O.L.
3A. Explain the correlation illustrated by the scatter plot. 3B. If there’s a correlation, justify whether the data sets might have a causal or non-causal relationship.
There is a no correlation between the two data sets.
The year has no impact on the number of hurricanes that may or may not appear
D.O.L.
4. Explain the correlation you would expect to see between each pair of data sets. Explain.
a. The outside temperature in the summer and the cost of the electric bill
Positive correlation; as the outside temperature increases, the electric bill increases because of the use of the air conditioner.
b. The price of a car and the number of passengers it seats
No correlation; a very expensive car could seat only 2 passengers.