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Quiz Unit 3


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

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

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

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.
  • The response variable is our dependent variable
    (traditionally y)?
  • The explanatory variable is our independent
    variable (traditionally x)?

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?

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.

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
  • DATA
  • Organize and examine the data. Answer the key
  • Construct appropriate graphical displays.
  • Calculate relevant summary statistics
  • Look for overall patterns and deviations
  • When the overall pattern is regular, use a
    mathematical model to describe it.

  • 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?

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

response variable
explanatory variable
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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.

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Interpreting Scatterplots
  • Direction?
  • Form?
  • Strength?
  • Outliers?

Adding Categorical Data
  • 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?

Making scatterplots on a calculator
  • See page 183

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
    widely scattered about a line.

  • 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.

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

Facts about Correlation
  • 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.

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

Cautionary Notes about Correlation
  • Correlation requires that both variables be
  • 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.

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
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