Investigating Scatter Plots Scatter plots – show correlations (relationships) between two...
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Transcript of Investigating Scatter Plots Scatter plots – show correlations (relationships) between two...
Investigating Scatter Plots
• Scatter plots –
show correlations (relationships) between two different pieces of data.
dependent variable (y’s or range) are affected by the independent variable
independent variable (x’s or domain) cause the change in dependent variable
Investigating Scatter PlotsWeight Loss Over Time
0
50
100
150
200
250
0 2 4 6 8 10 12
Days worked out per month
Weig
ht
Weight
1 3 5 7 9 11 13 15 170
20000
40000
60000
80000
100000
How shirts affect salary
Shirts Owned
Sa
lary
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 540
50
60
70
80
90
100
Chart Title
Series1
Hours Studying
Tes
t Gra
des
Data is collected and plotted on a graph
A pattern may be generally linear, but not form a perfect straight line.
Investigating Scatter Plots
• Positive correlations occur when two variables or values move in the same direction.
As the number of hours that you study increases your overall class grade increases
Investigating Scatter Plots – Positive Correlation
Study Time Class Grade
0 55
0.5 61
1 67
1.5 73
2 81
2.5 89
3 91
3.5 93
4 95
4.5 97
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 540
50
60
70
80
90
100
How Study Time Affects Grades
Time in hours
Ove
rall
gra
de
Investigating Scatter Plots
• Negative Correlations occur when variables move in opposite directions
As the number of days per month that you exercise increases your actual weight decreases
Investigating Scatter Plots – Negative Correlation
Weight Loss Over Time
0
50
100
150
200
250
0 2 4 6 8 10 12
Days worked out per month
Weig
ht
Weight
Work out time Weight
0 200
0.5 205
1 190
1.5 195
2 180
2.5 190
3 170
3.5 177
4 160
4.5 170
5 150
5.5 168
6 140
6.5 150
7 130
7.5 170
8 120
8.5 130
9 110
9.5 115
10 100
10.5 120
11 90
11.5 90
12 80
Investigating Scatter Plots
• No correlation exists if there is no noticeable pattern in the data
There is no relationship between the number of shirts someone owns and their annual salary
Investigating Scatter Plots – No Correlation
How does your wardrobe affect your salary
0
20
40
60
80
0 10 20 30 40 50
Number of shirts owned
Sal
ary
number of shirts owned salary
1 1
2 0
3 50
4 30
5 25
6 17
7 2
8 40
9 8
10 25
11 12
12 7
13 19
14 55
15 71
16 9
Line of Best Fit
• A line of best fit is a line that best represents the trend of the data on a scatter plot.
• A line of best fit may also be called a trend line
An equation of this line can be used to make predictions
The slope of the line is the average increase or decrease in y for every x
The y intercept is the value of y when x =0 The line may pass through some of the points,
none of the points, or all of the points.
Use the data to create a scatter plot
SandwichTotal Fat (g)
(X)Total Calories
(y)
Hamburger 9 260
Cheeseburger 13 320
Quarter Pounder 21 420
Quarter Pounder with Cheese 30 530
Big Mac 31 560
Arch Sandwich Special 31 550
Arch Special with Bacon 34 590
Crispy Chicken 25 500
Fish Fillet 28 560
Grilled Chicken 20 440
Grilled Chicken Light 5 300
Scatter Plot of the Data
Fat Grams and Calories in Food
0
100
200
300
400
500
600
700
0 5 10 15 20 25 30 35 40
Total Fat Grams
To
tal C
alo
rie
s
Using Graph Calculator for scatter plots and line of best fit• Reset your calculator 2nd , + , 7, 1, 2
• See “STAT PLOT” above Y=
• 2nd , Y =, enter, enter ( this turns plotter on )
• STAT, Enter, L1 are x’s, L2 are y’s
• Enter in your data for fat and calories
Using Graph Calculator for scatter plots and line of best fit• See “STAT PLOT” above Y=
• 2nd , Y =, enter, enter ( this turns plotter on )
• STAT, Enter, L1 are x’s, L2 are y’s
• Enter in your data for fat and calories
• Press Graph, (why cant I see anything?)
Using Graph Calculator for scatter plots and line of best fit• 2nd , Y =, enter, enter ( this turns plotter on )
• STAT, Enter, L1 are x’s, L2 are y’s
• Enter in your data for fat and calories
• Press Graph, (why cant I see anything?)
• Window, adjust settings
Xmin = 0
Xmax = 35
Ymin = 0
Ymax = 600
• Graph
Using Graph Calculator for scatter plots and line of best fitWe can have the calculator find an equation for
line of best fit, using linear regression.
• STAT, CALC, #4,
• Store the equation using ALPHA TRACE
• Graph
Now that we have an equation that models the data’s behavior, we can make predictions.
How many calories would expect a food item to have if it had 35 grams of fat?
about 604
Y = 11.73x + 193C = 11.73f + 193
• The slope is the average increase in Calories for every gm of fat (slope is average change in y for every x)
• The y intercept is the number of calories when a food item has no fat (y intercept is the value of y when x equals 0)
Things to remember• positive correlation has X and Y values that
rise together.
• negative correlation has X values that rise as Y values decrease
• no correlation has no visible relationship
• line of best fit is the line that best shows the trend of the data
• An equation of the line of best fit is a model of the data’s behavior and can be used to make predictions
• Slope if average increase in y for every x
• Y intercept is value of y when x = 0