Name ____________________________ Period
Section 4.4-Scatter Plots and Lines of Fit
Independent Variables
- Variable doesn’t depend on the other
- on the x-axis
- Usually happens first or is countable
- Time is almost always independent
Dependent
Dependent Variables
- variable depends on the other variable
- on the y-axis
- Usually happens second
Independent
Examples: Label the independent and dependent variables. Then name its correlation
1) Hours worked ________
Money made __________
Correlation __________
2) Heart Rate ________
Age ___________
Correlation __________
3) Grade your in ________
# of pets your own ________
Correlation __________
Questions:
What variable goes on the x axis? ___________
What variable goes on the y- axis? ___________
How many possible independent variables are there in any situation? ___________
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Scatter plots Activity
Name
Date
Period
The relationship between the cost of renting a car from the Wrecko Car Rental Company
and number of days for the rental is shown below.
Days
Rental $
1
30
2
53
3
76
4
99
7
168
10
237
a) Title the graph
b) Write the independent variable (Days) on the x-axis,
and the dependent variable (Rental$) on the y-axis.
c) Number the x-axis and the y-axis
Ex: 1 2 3 4 5… Ex: 2 4 6 8 10… Ex: 10 20 30 40 50…
d) Plot your points from the data in the table
e) Draw a bet fit line through the points
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Scatterplots and Trend lines
Would you expect a positive correlation, a negative correlation or no correlation?
1. a person’s age vs the number of pets
2. Number of times you brush your teeth vs. number of cavities
3. Number of days a year it rains vs. number of umbrellas sold
4.
5.
6.
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Name _________________________________________________________ Date _________
4.4
Practice A
1. The scatter plot shows students' scores for Quiz 1 and Quiz 2.
a. What is the Quiz 1 score for a student who earned a score of 13 on Quiz 2?
b. Did any student(s) earn the same score on both Quiz 1 and Quiz 2?
Explain.
c. Does there appear to be a difference between the Quiz 1 scores and the Quiz 2 scores?
Explain.
In Exercises 2 and 3, tell whether x and y show a positive, a negative, or no correlation.
2.
3.
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Name _________________________________________________________ Date _________
4.4
Practice B
1. The scatter plot shows the prior bowling averages of competitors at the bowling tournament and
their highest scores during the tournament.
a. How many competitors bowled above their average during the tournament?
b. Did any bowler(s) bowl their average as their highest score? Explain.
c. What are the scores of the competitors with the greatest difference between their bowling
average and their highest score?
In Exercises 2 and 3, tell whether x and y show a positive, a negative, or no correlation.
2.
3.
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Section 4.5-Analyzing Lines of Fit
How to find the equation on a line in the graphing calculator:
I.
Press STAT, select 1: EDIT
Press: ENTER
Record Table values into L1 and L2
II.
Press STAT
Arrow over to CALC
Arrow down to: Linear Regression
Press ENTER
Arrow down to Calculate
Press ENTER
Line will be given as y = ax + b
“a” represents the slope (Rate of change)
“b” represents the y-intercept (Beginning/Initial value)
2nd Catalog
DiagnosticON
Done
Round to tenths place
Y = 0.9x + 13.7
1. The table shows the number y of pineapple plants in a garden x years since 2004.
x
2
3
4
7
8
9
y
4
7
9
15
16
19
a. Write an equation that models the approximate number of pineapple plants
as a function of the number of years since 2004.
b. Interpret the slope and y-intercept of the line of fit.
2. The table shows the total number y of rolls of wrapping paper sold by a student after x weeks.
x
1
2
3
4
5
6
y
3
5
9
12
17
24
a. Write an equation that models the number of rolls of wrapping paper
as a function of the number of weeks.
b. Interpret the slope and y-intercept of the line of fit.
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Correlation
Positive correlations
Go ______ from left to right, and as one variable increase the other _______________
Negative correlations
Go ______ from left to right, and as one variable increase the other _______________
Correlation Coefficient can be found from the residual variable “r” in a linear regression
Correlation Coefficient:
Strong if close to 1 or -1, Points close together
Weak if close to zero, Points not close together
Round to hundredths place
R = .98
Strong Positive Correlation
Calculator Reminder:
I. Stat Edit
II. Stat, Calc, Linear Regression
III. Calculate
Find and describe the correlation coefficient:
x
7
5
3
1
0
1
3
5
7
x
12
9
6
3
0
3
6
9
12
y
26
22
15
8
7
3
4
8
16
y
27
15
2
6
21
30
42
58
67
80
Name _________________________________________________________ Date _________
Use a graphing calculator to find an equation of the line of best fit for the data.
Identify and interpret the correlation coefficient.
1.
2.
3.
4.
x
1
2
3
4
5
6
7
8
9
y
7
4
1
0
0
1
4
7
9
x
5
3
1
1
3
5
7
9
11
y
20
18
15
14
12
9
7
4
2
x
12
8
4
0
4
8
12
16
20
y
48
42
37
31
29
24
19
14
7
x
3
4
5
6
7
8
9
10
11
y
20
36
15
32
12
28
17
16
24
5. The table shows the number of people x in a room and the temperature in the room in degrees
Fahrenheit, y.
x
0
1
2
3
4
5
6
7
8
y
76
76
77
77
78
79
79
80
82
a. Use a graphing calculator to find an equation of the line of best fit.
b. Identify and interpret the correlation coefficient.
c. Approximate the temperature when 15 people are in the room.
6.
The table shows the average number of minutes y per kilometer for runners and the total distance of a running
race, x (in kilometers).
x
3.1
6.2
9.3
12.4
15.5
18.6
21.7
24.8
27.9
y
5.4
5.6
5.7
5.9
6.0
6.1
6.3
6.5
6.9
a. Use a graphing calculator to find an equation of the line of best fit.
b. Identify and interpret the correlation coefficient.
c. Approximate the average number of minutes per kilometer when
the distance of a race is 31 kilometers.
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Correlation and Causation
Just because two things are correlated, doesn’t mean that one caused the other.
Tell whether correlation is likely. If so, tell whether there is a causal relationship (causation).
1. Time spent exercising, the number of calories burned
2. The weight of a dog and the length of its tail
3. The amount of time spent talking on a cell phone and the remaining battery life
4. The height of a toddler and the size of the toddler’s vocabulary
5. The number of hats you own and the size of your head
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Name the independendent and dependent variable:
1) The number of employees and the number of CD’s produced
Independent______________________
Dependent________________________
2) The amount of wallpaper and the size of the room
Independent______________________
Dependent________________________
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EOC Questions
1) The graph relates the cost to mail a
letter with the weight of the letter.
Which statement is true:
a) The mailing cost depends on the weight of the letter
b) The weight of the letter depends on the mailing cost
c) The mailing cost and weight depend on the number
of letters being mailed
d) The number of letters being mailed depends on
the mailing cost and weight
2) Gloria plans to burn a 12-inch candle for a few hours. The height of the candle decreases at the same rate
each hour. Gloria writes an equation to model the height of the burning candle for each hour it burns. What
is the dependent variable in this equation?
a) the original height of the candle
b) the height of the burning candle
c) the rate the candle burns each hour
d) the number of hours the candle burns
3) The scatter plot above shows the relationship between protein and fiber in certain foods. Which statement is
true of the protein and fiber content in these foods?
a) Most have close to 1 gram of protein
b) Most have more than 4 grams of fiber
c) Most have more grams of protein than fiber
d) Most have more grams of fiber than protein
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a)
4) The scatter plot above shows the ages of used cars and their
prices. Which statement is best supported by this data?
a) Most used cars cost less than $14,000
b) The oldest used car has the lowest price
c) Most used cars are less than 3 years old
d) The price of a used car steadily decreases with age
5) The area formula for a circle is A=πr2, how many independent variables are there?
a) none
b) one
c) two
d) three
6) Ben builds custom ladders of varying heights. He uses this equation to
determine the number of rungs, r, to put on a ladder that has a height of h
feet.
r = h ÷ 0.8
What is the independent variable in this situation?
a) the height of the ladders
b) the number of ladders
c) the space between the rungs on the ladder
d) the total number of rungs on the ladder
7) Which scatter plot best represents the data in the table below?
b)
c)
d)
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