Top 10 Things to Remember about Summarizing Bivariate Data

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Top 10 Things to Remember about Summarizing
Bivariate Data
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10. Always make a picture

• (scatterplot of data, residual plot)

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9. Identify the explanatory and response
variables.

• (either in your equation or define the variables
  separately)

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True or FalsePearsons correlation coefficient,
r, does not depend on the units of measurement of
the two variables.
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True or FalseThe value of Pearsons correlation
coefficient, r, is always between 0 and 1.
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8. If the goal is to describe the strength of
relationship, report correlation coefficient.
(strength, direction, form, and unusual features,
always in context)
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7. If the goal is to predict, report the LSRL and
coefficient of determination.
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True or FalseThe slope of the least squares
line is the average amount by which y increases
as x increases by one unit.
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True or FalseThe slopes of the LSRL for
predicting y from x, and the LSRL for predicting
x from y, are equal.
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6. Explain what the slope b and y-intercept mean
in CONTEXT in the predicted y a bx
regression line.
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5. Beware of extrapolation (do not assume that a
linear model is valid over a wider range of x
values)
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True or FalseThe LSRL passes through the point
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True or FalseThe coefficient of determination
is equal to the positive square root of Pearsons
r.
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4. A correlation coefficient of 0 does not
necessarily imply that there is no relationship
between two variables (could be strong but not
linear).
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3. Watch out for influential observations. (pulls
LSRL toward it, but will be close to 0 in
residual plot)
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True or FalseIf r 1, the standard deviation
of y is equal to the standard deviation of the
residuals.
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True or FalseThe standard deviation about the
LSRL is roughly the typical amount by which an
observation deviates the least squares line.
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True or FalseA transformation (or reexpression)
of a variable is accomplished by substituting a
function of the variable in place of the variable
for further analysis.
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True or FalseThe higher the value of the
coefficient of determination, the greater the
evidence for a causal relationship between x and y
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2. Correlation does not imply causation. A
strong correlation implies only that the two
variables tend to vary together in a predictable
way.
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And the 1 thing to remember.
1. Only use QUANTITATIVE data when comparing
bivariate data
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Plot your data. (scatterplot)
Interpret what you see. (direction, form,
strength, outliers)
Numerical summary?
Mathematical model? (Regression line)
How well does it fit? (Residuals and r2)
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• Given this residual plot, which of the following
  is not a correct conclusion?
• a) The pattern in the residuals indicates the
  regression line does not fit the data well.
• b) Point A is a candidate as an outlier.
• c) Point A is a candidate as an influential
  point.
• d) The relationship between the variables is
  positive.
• e) All of these are correct.

Residuals
Fitted values
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2) Which of the following residual plots
indicates a reasonable fit to a given set of
data? a) c)
b) d) e) None of these indicates a
reasonable fit.
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• 3) Which of the following is a correct conclusion
  based on the residual plot displayed?
• The line overestimates the data.
• b) The line underestimates the data.
• c) It is not appropriate to fit a line to these
  data since there is clearly no correlation
  between the variables.
• d) The data is not related.
• e) None of these choices is correct.

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• 5) You are given the regression equation
• temperature 30.4 - .72(distance), where
  temperature is the temperature displayed on a
  sensor in C and distance is the distance in
  centimeters from the sensor to a heat source.
  Which of the following is not a reasonable
  conclusion?
• The temperature of the heat source is
  approximately 30.4C.
• b) The temperature decreases approximately .72C
  for each centimeter the sensor is moved away from
  the heat source.
• c) We can predict that the sensor displays a
  temperature of 21.76C when the sensor is 12
  centimeters away from the heat source.
• d) The correlation coefficient between
  temperature and distance indicates a negative
  relationship.
• e) All of these are reasonable.

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• 7) If the correlation coefficient of a bivariate
  set of data (x,y) is r, then which of the
  following is true?
• The variable x and y are linearly related.
• b) The correlation coefficient of the set (y,x)
  is also r.
• c) The correlation coefficient of the set
  (x,ay) is also a ?r.
• d) The correlation coefficient of the set
  (ax,ay) is also a ?r.
• e) None of these is true.