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## Quiz Unit 3

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### Quiz Unit 3 Find the proportion of observations from a standard Normal distribution that fall in each of the following regions. In each case, sketch a standard Normal ... – PowerPoint PPT presentation

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Title: Quiz Unit 3

1
Quiz Unit 3
• Find the proportion of observations from a
standard Normal distribution that fall in each of
the following regions. In each case, sketch a
standard Normal curve and shade the area
representing the region.
• 1. zlt0.83
• 2. zgt-1.0
• 3. zgt-1.56

2
The Practice of Statistics
• Unit 4/ Chapter 3
• Examining Relationships

3
Examining Relationships
• When are some situations when we might want to
examine a relationship between two variables?
• Height Heart Attacks
• Weight Blood Pressure
• Hours studying test scores
• What else?

In this chapter we will deal with relationships
and quantitative variables the next chapter will
deal with more categorical variables.
4
• The response variable is our dependent variable
• The explanatory variable is our independent

5
Explanatory or Response?
• Which is the explanatory and which is the
response variable?
• Jim wants to know how the mean 2005 SAT Math and
Verbal scores in the 50 states are related to
each other. He doesn't think that either score
explains or causes the other.
• Julie looks at some data. She asks, Can I
predict a state's mean 2005 SAT Math score if I
know its mean 2005 SAT Verbal score?

6
Explanatory and Response Variables
• When we deal with cause and effect, there is
always a definite response variable and
explanatory variable.
• But calling one variable response and one
variable explanatory doesn't necessarily mean
that one causes change in the other.

7
When analyzing several-variable data, the same
principles appy Data Analysis Toolbox
• To answer a statistical question of interest
involving one or more data sets, proceed as
follows.
• DATA
• Organize and examine the data. Answer the key
questions.
• GRAPHS
• Construct appropriate graphical displays.
• NUMERICAL SUMMARIES
• Calculate relevant summary statistics
• INTERPRETATION
• Look for overall patterns and deviations
• When the overall pattern is regular, use a
mathematical model to describe it.

8
Scatterplots
• Let's say we wanted to examine the relationship
between the percent of a state's high school
seniors who took the SAT exam in 2005 and the
mean SAT Math score in state that year. A
scatterplot is an effective way to graphically
represent our data.
• But first, what is the explanatory variable and
what is the response variable in this situation?

9
Scatterplots
• Once we decide on the response and explanatory
variables, we can create a scatterplot.

response variable
explanatory variable
10
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11
Scatterplot Tips
• Plot the explanatory variable on the horizontal
axis. If there is no explanatory-response
distinctions, either variable can go on the
horizontal axis.
• Label both axes!
• Scale the horizontal and vertical axes. The
intervals must be uniform.
• If you are given a grid, try to adopt a scale so
that your plot uses the whole grid. Make your
plot large enough so that the details can be
easily seen.

12
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13
positive
negative
14
Interpreting Scatterplots
• Direction?
• Form?
• Strength?
• Outliers?

15
• The Mean SAT Math scores and percent of hish
school seniors who take the test, by state, with
the southern states highlighted.
• Is the South different?

16
Making scatterplots on a calculator
• See page 183

17
Measuring Linear Association Correlation
• Linear relations are important because, when we
discuss the relationship between two quantitative
variables, a straight line is a simple pattern
that is quite common.
• A strong linear relationship has points that lie
close to a straight line.
• A weak linear relationship has points that are

18
• Our eyes are not good measures of how strong a
linear relationship is...
• A numerical measure along with a graph gives the
linear association an exact value.

19
In words, standardize each value, multiply
corresponding values, add them up, and divide by
n-1
20
Correlation Regression Applet www.whfreeman.com/
tps3e Pg190
• Correlation on the calculator.

21
• Correlation makes no distinction between
explanatory and response variables.
• r doesn't change when we change the units of
measurement of x, y, or both.
• r is positive when the association is positive
and is negative when the association is negative.
• The correlation r is always a number between -1
and 1. Values of r near 0 indicate a very weak
linear relationship. The strength of the linear
relationship increases as r moves away from 0
toward either -1 or 1.

22
• Patterns closer to a straight line have
correlations closer to 1 or -1

23
• Correlation requires that both variables be
quantitative.
• Correlation does not describe curved
relationships, no matter how strong they are.
• Like the mean and standard deviation, the
correlation is not resistant r is strongly
affected by a few outlying observations.
• Correlation is not a complete summary of
two-variable data. You should give the means and
standard deviations of both x and y along with
the correlation.

24
Scoring Figure Skaters
• Until a scandal at the 2002 Olympics brought
change, figure skating was scored by judges on a
scale from 0.0 to 6.0. The scores were often
controversial. We have the scores awarded by two
judges, Pierre and Elena, for many skaters. How
well do they agree? We calculate that the
correlation between their scores is r 0.9. The
mean of Pierres scores is 0.9 point lower than
Elenas mean. Do these facts contradict each
other?