Transcript Linear Regression - mrscoachaldridge

Linear Regression
AP Statistics
Chapter 8 & 9 Day 3
Read the two articles.
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Free Write: What is your personal opinion about
the current state of gun control in the US? What
changes, if any, would you make? Why? Are
assault weapons to blame for the recent mass
killings? How would you conduct a study to
determine the relationship?
What can go wrong?
Make sure the relationship is straight.
 Beware of extrapolating.
 Look for unusual points.
 Beware of influential points.
 Linear models do not prove causation.
 Don’t choose a model based on r² alone
 Always check conditions and look at the
scatterplot.
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Vocabulary
Extrapolation
 Outlier
 Influential point
 Lurking variables
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1.
Which of the following statements about
outliers is true?
I. Removing an outlier from a data set can
have a major effect on the regression line.
II. If you calculated the residual between the
outlier and a regression line based on the rest
of the data, it would probably be large.
III. You will typically find an outlier horizontally
distant from the rest of the data along the xaxis.
2.
Which of the following statements about
influential points is true?
I. Removing an influential point from a data
set can have a major effect on the
regression line.
II. If you calculate the residual between the
influential point and a regression line based
on the rest of the data, it will probably be
large.
III. You will typically find an influential point
horizontally distant from the rest of the data
along the x-axis.
3.
A proper interpretation of a coefficient of determination
of 0.754 is:
A. 75.4% of the variation in the response variable can
be explained by our knowledge of the explanatory
variable.
B. 75.4% of the variation in the explanatory variable
can be explained by our knowledge of the response
variable.
C. The amount of variation in the response variable is
reduced by 24.6%.
D. For each unit increase in the explanatory variable,
the response variable increases 75.4%.
E. None of the above.
4.
The goal of the least-squares regression
is to compute a line that:
A. Connects all the bivariate data points
in a scatterplot
B. Connects all the residuals shown in a
scatterplot
C. Minimizes the sum of the observed
values of x and y.
D. Minimizes the sum of the squared
residuals.
E. None of the above.
Suppose that you have a bivariate data set
and the correlation coefficient for the
relationship between x and y is strong.
Suppose also that you compute a LSRL that
seems to fit the linear pattern in this bivariate
data. You decide to plot the observed x-values
against the residuals. If the pattern in the data
is truly linear, you should find that the
residuals:
A. Follow a u-shaped pattern
B. Are randomly distributed around the line
y-hat = 0
C. Follow a linear pattern
D. Are clumped at values above the line y-hat =0
E. Do all of the above
5.
Homework
Page 193 #23, 24
 Page 194 # 25, 28, 32, 37, 39, 46, 53
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