Scatter Plots

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Scatter Plots

• Best Fit Lines To Make Predictions

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Using a Rule

• We have learned that a rule can be used to make
  predictions.
• Remember, If your paycheck is calculated by 8
  times the number of hours you work (P 8h), then
  you could calculate how much you would make in a
  40 hour week.
• You could also do that from the graph of the line
  produced from that rule.

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Table and Graph (P 8h)
h P
0
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Using a Rule

• To make the graph, you plotted the points, then
  you drew a line that passed through the points.
• Because the last situation was calculated using a
  rule, the line was able to touch each point.
• Notice the line went up from left to right. That
  is called Positive Slope.

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Using a Rule

• Suppose you are on a diet and loose 2 lbs. each
  week.
• Your weight can be calculated by the rule
• T -2w Beginning Weight
• Plot the points and graph the total weight loss .
  Suppose your Beginning Weight is 150 lbs.

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Using a Rule (T -2w Beginning Weight)
w T
0
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15
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Using a Rule

• To make the graph, you plotted the points, then
  you drew a line that passed through the points.
• Because the last situation was calculated using a
  rule, the line was able to touch each point.
• Notice the line went down from left to right.
  That is called Negative Slope.

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No Rule

• Scatterplots do not always follow a rule.
• Even without a rule, a scatterplot can follow a
  pattern.
• We are going to look at three patterns.
• Positive Correlation
• Negative Correlation
• No Correlation

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Economic Levels Vs. College Education

• Suppose our class was going to conduct a survey.
• We are going to find out how much college
  education each person had and their current
  economic level.
• Do you think there is a relationship?
• If so, is there always a relationship?
• For this example we are going to use 5 levels of
  economic level.
• College Educations consists of
• No Degree
• Associate Degree
• Bachelor Degree
• Masters Degree
• Doctorate Degree

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Economic Levels Vs. College Education

• Things to think about.
• Does everybody with no college education have an
  economic level of 1?
• Does everybody with a Bachelors Degree have an
  economic level of 3?
• The answer to both of these is no, but in most
  cases, this would be a good guess.
• When creating your table, keep this in mind, most
  of your points should follow the norm, but some
  will stray.

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Graph
Not all points will be exact.
Some points will stray.
These points are the norm.
Economic Level
College Education
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Scatterplots

• Notice all the points do not line up like when
  you follow a rule.
• They do follow a pattern though.
• Notice like the graph of the Paycheck, the
  economic level generally increases as the college
  education increases.
• Like the other graph, this is a positive
  relationship. With a scatterplot like this, we
  call it a Positive Correlation.

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Best Fit Lines

• By drawing a line that comes closest to all of
  the points, not necessarily touching them, we can
  make predictions for bigger numbers.
• This is called a best fit line

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Best Fit Lines

• Have you ever heard the news report a survey that
  says, America believes ?
• If so, did they ask you?
• Instead of surveying every person in the U.S.
• They survey a small random group
• Graph a scatterplot
• Draw a best fit line to make predictions for the
  entire U.S. population.

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Age Vs. Cost of Car Insurance

• Assume the norm for a 25 year old will cost about
  150 every month.
• Only find values for some of the ages, then draw
  a best fit line to make predictions for the rest.

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Graph
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Correlation

• What type of correlation do these quantities
  have?
• How can you explain this verbally?
• How can you explain this by using the graph.

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Shoe Size Vs. IQ
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(No Transcript)
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Correlation

• What type of correlation do these quantities
  have?
• How can you explain this verbally?
• How can you explain this by using the graph.

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Positive, Negative, or No Correlation? Use a
best fit line to make predictions
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Positive, Negative, or No Correlation? Use a
best fit line to make predictions
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Positive, Negative, or No Correlation? Use a
best fit line to make predictions
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Positive, Negative, or No Correlation? Use a
best fit line to make predictions
25
Identify the correlation you would expect to see
between the pair of data sets. Explain.
the average temperature in a city and the number
of speeding tickets given in the city
You would expect to see no correlation. The
number of speeding tickets has nothing to do with
the temperature.
26
Identify the correlation you would expect to see
between the pair of data sets. Explain.
the number of people in an audience and ticket
sales
You would expect to see a positive correlation.
As the number of people in the audience
increases, ticket sales increase.
27
Identify the correlation you would expect to see
between the pair of data sets. Explain.
a runners time and the distance to the finish
line
You would expect to see a negative correlation.
As a runners time increases, the distance to the
finish line decreases.
28
Identify the type of correlation you would expect
to see between the pair of data sets. Explain.
the temperature in Houston and the number of cars
sold in Boston
You would except to see no correlation. The
temperature in Houston has nothing to do with the
number of cars sold in Boston.
29
Identify the type of correlation you would expect
to see between the pair of data sets. Explain.
the number of members in a family and the size of
the familys 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.
30
Identify the type of correlation you would expect
to see between the pair of data sets. Explain.
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.
31
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
32
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
33
The scatter plot shows a relationship between the
total amount of money collected at the concession
stand and the total number of tickets sold at a
movie theater. Based on this relationship,
predict how much money will be collected at the
concession stand when 150 tickets have been sold.
Draw a trend line and use it to make a prediction.
Draw a line that has about the same number of
points above and below it. Your line may or may
not go through data points.
Find the point on the line whose x-value is 150.
The corresponding y-value is 750.
Based on the data, 750 is a reasonable
prediction of how much money will be collected
when 150 tickets have been sold.
34
Based on the trend line, predict how many
wrapping paper rolls need to be sold to raise
500.
Find the point on the line whose y-value is 500.
The corresponding x-value is about 75.
Based on the data, about 75 wrapping paper rolls
is a reasonable prediction of how many rolls need
to be sold to raise 500.