Day 1
y axis
 Measures an outcome of a study
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X axis
 Attempts to explain the observed
outcomes
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(a) The amount of time a student spends studying
for a statistics exam and the grade on the exam.
What is the explanatory variable?
Explanatory variable: time spent studying
What is the response variable?
Response variable: grade on the exam
(b) The weight and height of a person
Think about it!
Weight effects height and height effects weight.
They do not have a set explanatory/response
relationship. It could go either way!
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(c) The amount of yearly rainfall and the yield
of a crop.
Explanatory Variable?
yearly rainfall
Response Variable?
crop yield
(d) A students grades in Statistics and French
Think about it!
do not have an explanatory/response
relationship at all.
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(e) The occupational class of a father and a son.
Explanatory Variable?
The father’s class
Response Variable?
The son’s class
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Shows the relationship between two
quantitative variables measured on the same
individuals. The values of one variable appear
on the horizontal axis and the values of the
other appear on the vertical axis.
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Scale the horizontal and vertical axes. The
intervals must be uniform; tat is the distance
between the intervals must be the same. If the scale
does not begin at zero at the origin, then use the
symbol shown to indicate a break.
Label both axes.
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.
Don’t compress the plot into one corner of the grid.
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In any graph of data, look for the overall
pattern and for striking deviations from that
pattern
You can describe the overall pattern of a
scatterplot by the form, direction and shape of
the relationship.
An important kind of deviation is an outlier, an
individual value that falls outside the overall
pattern of the relationship.
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Two variables are
positively associated
when above average
values of one tends to
accompany above
averages of the other
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Two variables are
negatively associated
when above average
values of one tends to
accompany below
average values of the
other and vice versa.
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The Sanchez Household is about to install
solar panels to reduce the cost of heating
their household. In order to know how
much the solar panels help; they record
their consumption of natural gas before
the panels are installed. Gas
consumption is higher in cold weather so
the relationship between outside
temperature and gas consumption is
important.
The following table shows the degreedays per month and the gas consumed.
A degree-day is the usual measure of
demand for heating. One degree day is
accumulated for each degree a day’s
average temperature falls below 65
degrees F. An average temperature of 20
degrees F for example corresponds to 45
degree days
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The Sanchez Household is about to install
solar panels to reduce the cost of heating
their household. In order to know how
much the solar panels help; they record
their consumption of natural gas before
the panels are installed. Gas
consumption is higher in cold weather so
the relationship between outside
temperature and gas consumption is
important.
The following table shows the degreedays per month and the gas consumed.
A degree-day is the usual measure of
demand for heating. One degree day is
accumulated for each degree a day’s
average temperature falls below 65
degrees F. An average temperature of 20
degrees F for example corresponds to 45
degree days
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What is the explanatory
variable and what is the
response?
Explanatory variable:
the average number of
degree days each day
during the month.
Response Variable: the
average amount of
natural gas consumed
each day during the
month.
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Draw the scatterplot:
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Interpret the plot. (State,
explain)
The graph shows a positive
association. More degreedays means colder weather
and so more gas consumed.
The form of the relationship
is linear. That is, the points
lie in a straight-line pattern.
It is a strong relationship.
That is, the points lie close to
a line with little scatter.
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NOT ALL RELATIONSIPS HAVE A CLEAR
DIRECTION THAT CAN BE DESCRIBED
AS POSITIVE OR NEGATIVE.
STRENGTH IS DETERMINED WITH HOW
SPREAD OUT THE POINTS ARE. A
STRONG RELATIONSHIP LIES CLOSE TO
A LINE WHERAS A WEAK RELATIONSHIP
IS MORE SPREAD OUT. WE WILL SEE
THIS SOON ENOUGH IN THE NEXT
SECTION.