scatter plots and trend lines · scatter plots and trend lines 10 march 02, 2016 feb 2310:10 am...
TRANSCRIPT
Scatter Plots and Trend Lines
1
March 02, 2016
Feb 239:13 AM
2/29/16 Warm Up
A student says the equation y = 4x + 1 can be written in standard form as 4x y = 1. Describe and correct the student's error.
Scatter Plots and Trend Lines
2
March 02, 2016
Feb 239:12 AM
Unit 5: Linear Functions
Scatter Plots and Trend Lines
Scatter Plot: a graph that relates two different sets of data by displaying them as ordered pairs.
Scatter Plots and Trend Lines
3
March 02, 2016
Feb 239:18 AM
Making a Scatter Plot and Describing its Correlation
(pg. 337)Example: The table shows the altitude of an airplane and the temperature outside the plane.
a. Make a scatter plot of the data.
b. What time of relationship does the scatter plot show?
0 500 100015002000250030003500400045005000
10
20
30
40
50
60
x
y
Scatter Plots and Trend Lines
4
March 02, 2016
Feb 239:32 AM
Practice: Make a scatter plot of the data in the table below. What type of relationship does the scatter plot show?
0 2 4 6 8 10 12 14 16
1
2
3
4
x
y
Scatter Plots and Trend Lines
5
March 02, 2016
Feb 239:38 AM
Practice: Consider the population of a city and the number of letters in the name of the city. Would you expect a positive correlation, a negative correlation, or no correlation between the two sets of data? Explain.
Scatter Plots and Trend Lines
6
March 02, 2016
Feb 239:40 AM
Trend Line: a line on a scatter plot, drawn near the points, that shows a correlation
Interpolation: estimating a value between two known values
Extrapolation: predicting a value outside the range of known values
Scatter Plots and Trend Lines
7
March 02, 2016
Feb 239:44 AM
Writing an Equation of a Trend Line (pg. 338)
Example: Make a scatter plot of the data shown. What is the approximate weight of a 7month old panda?
After creating a scatter plot, write an equation of the trend line find the slope and plug it into pointslope form to create an equation
Use the equation to estimate the weight at 7 months.
0 1 2 3 4 5 6 7 8 9 10 11 12
6
12
18
24
30
36
42
48
54
60
x
y
Scatter Plots and Trend Lines
8
March 02, 2016
Feb 239:50 AM
Practice: Make a scatter plot of the data shown. Draw a trend line and write its equation.
0 1 2 3 4 5 6 7 8 9 10
5
10
15
20
25
30
35
x
y
What is the approximate body length of a 7month old panda?
Scatter Plots and Trend Lines
9
March 02, 2016
Feb 2310:03 AM
Line of Best Fit: the trend line that shows the relationship between two sets of data most accurately
Correlation Coefficient: a number from 1 to 1, that tells how closely the equation models the data
The nearer r is to 1 or 1, the more closely the data cluster around the line of best fit. If r is near 1, the data lie close to a line of best fit with a positive slope. If r is near 1, the data lie close to a line of best fit with a negative slope.
Scatter Plots and Trend Lines
10
March 02, 2016
Feb 2310:10 AM
Finding the Line of Best Fit (pg. 339)
Example: Use a graphing calculator to find the equation of the line of best fit for the data shown. What is the correlation coefficient to three decimal places? Predict the cost of attending in the 20122013 academic year.
Scatter Plots and Trend Lines
11
March 02, 2016
Feb 2310:26 AM
To predict the cost of attending in the 20122013 academic year, use the information from the calculator to create an equation in slopeintercept form. Then plug in the year for x.
Scatter Plots and Trend Lines
12
March 02, 2016
Feb 2310:31 AM
What would the cost most likely be for attending in the 20162017 academic year?
Scatter Plots and Trend Lines
13
March 02, 2016
Feb 2310:33 AM
Causation: when a change in one quantity causes a change in a second quantity
* A correlation does not always imply a causation.
Scatter Plots and Trend Lines
14
March 02, 2016
Feb 2310:37 AM
Identifying Whether Relationships Are Causal (pg. 340)
Example: In the following situations, is there likely to be a correlation? If so, does the correlation reflect a causal relationship? Explain.
a. the number of loaves of bread baked and the amount of flour used
b. the number of mailboxes and the number of firefighters in a city
c. the amount of ice cream sold on the boardwalk and the number of shark attacks
Scatter Plots and Trend Lines
15
March 02, 2016
Feb 2310:41 AM
Practice: In the following situations, is there likely to be a correlation? If so, does the correlation reflect a causal relationship? Explain.
a. the cost of a family's vacation and the size of their house
b. the time spent exercising and the number of Calories burned
c. the amount of ice cream sold on the boardwalk and the outside temperature
Scatter Plots and Trend Lines
16
March 02, 2016
Feb 2310:48 AM
HOMEWORK: pg. 341 #7, 8, 9, 11, 12, 14, 15
Scatter Plots and Trend Lines
17
March 02, 2016
Feb 267:54 AM
0 1 2 3 4 5 6 7 8 9 10200
220
240
260
280
300
320
340
x
y