Download Scatter Plot Correlation

Scatter Plots
A graph of a set of data
pairs (x, y)
Correlation Coefficient, r
A number, denoted by r, from
-1 to 1 that measures the
strength and direction of a
linear relationship between
two variables
3 Types of Correlation
Positive
Negative
No Correlation
Positive Correlation
Relationship between
paired data when y tends
to increase as x increases
Negative Correlation
Relationship between
paired data when y tends
to decrease as x
increases
No Correlation (or Zero Correlation)
The points do not lie close
to any line
Strong Positive Correlation
The points are
clustered
resembling a
rising straight
line with a
positive
slope.
r is close to +1
http://www.regentsprep.org/regents/math/algebra/AD4/scatter.htm
Weak Positive Correlation
Points tend to
rise, but this is
a weak
positive slope
Strong Negative Correlation
The points are
clustered
resembling a
falling straight
line with a
negative
slope.
r is close to -1
Weak Negative Correlation
Points tend to
fall, but this is
a weak
negative
slope
No way to
determine
and no
straight line
forms
1. The scatter plot shows a relationship
between hours worked and money earned.
Which best describes the relationship
between the variables?
Strong Positive
Correlation
2. The scatter plot shows a relationship
between age and height.
Which best describes the relationship
between the variables?
No
Correlation
3. The scatter plot shows a relationship
between age of a car and its value.
Which best describes the relationship
between the variables?
Weak
Negative
Correlation
4. The scatter plot shows a relationship
between number of customers and the
temperature.
Which best describes the relationship
between the variables?
Weak Positive
Correlation
Some Types of Regression
Linear Regression - straight
line form
Some Types of Regression
Quadratic Regression
parabolic form (u-shape)
Linear Regression
A method for finding the
equation of the
best-fitting line,
1. Which choice is the best
example of a line of best fit?
2. Matt considers whether or not the amount
of time students study for a test are related.
He determines that the more they study the
higher grade they will get. What type of
slope would the line of best fit have?
A.
B.
C.
D.
negative
positive
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zero
3. What type of model best
describes this data’s relationship?
A.
B.
C.
D.
Linear
Quadratic
Exponential
No
relationship
Hint: look at the rate of increase…is it constant?
4. What type of model best
describes this data’s relationship?
A.
B.
C.
D.
Linear
Quadratic
Exponential
No
relationship
Hint: look at the rate of increase
5. What type of model best
describes this data’s relationship?
A.
B.
C.
D.
Linear
Quadratic
Exponential
No
relationship
6. The graph shows Jessica’s weight as it
compares to her age. Using the line of
best fit, what is the best approximation for
her weight at age 9
A.
B.
C.
D.
70
75
80
85
7. The table shows the average household
size y in the U.S. from 1930 to 2000.
y = -.021t + 3.9425
Years since Household
1930, t
0
size, y
4.11
10
3.67
20
3.37
30
3.35
40
3.14
50
2.76
60
2.63
70
2.62
Use the model and
predict the average
household size in
2030.
(2030 – 1930) and
substitute that in for t
1.84
Consumer Debt
The table shows the total outstanding
consumer debt (excluding home mortgages)
in billions of dollars in selected years. (Data is
from the Federal Reserve Bulletin.)
Years since
1985
Consumer
Debt (billions)
0
5
585
789
10
15
1096 1693
Let x = 0 correspond to 1985.
The best fit line is
y  79.859 x  463.35
18
1987
y  79.859 x  463.35
8. Find the approximate consumer
debt in 1998. 1998  1985
1501.517 billion
9. Find the approximate consumer
debt in 2008.  2008  1985
2300.107 billion
Health
The table below shows the number of deaths per
100,000 people from heart disease in selected
years. (Data is from the U.S. National Center for
Health Statistics.)
Years since
1960
Deaths
0
10
20
30
40
42
559
483
412
322
258
240
Let x = 0 correspond to 1960.
The line of best fit is
y  7.62 x  559.25
y  7.62 x  559.25
10. Find an approximation for the
number of deaths due to heart disease
in 1995.
1995  1960
293
11. Predict the number of deaths from
heart disease in 2008.
 2008 1960 193 almost 194
12. Which equation best fits the
scatterplot?
A. f(x)  (x  3)2  4
C. f(x)  (x  4)2  3
B. f(x)  (x  3)2  4
D. f(x)  (x  4)2  3
13. Which equation best fits the
scatterplot?
A. f(x)  x2  8 x  22
C. f(x)   x2  8 x  32
B. f(x)   x2  8 x  10
D. f(x)   x2  8x  10
14. Which equation best fits the
scatterplot?
2
2
A. f(x)  (x  25)  5
C. f(x)  (x  25)
B. f(x)  41 (x  25)2  5
D. f(x)  41 (x  25)2
1
4
1
4
15. What type of model would
best fit the data?
A.
B.
C.
D.
Linear
Quadratic
Exponential
Cubic
16. What type of model would
best fit the data?
A.
B.
C.
D.
Linear
Quadratic
Exponential
Cubic