In class Review for the Final
#1
24.36 Sparrowhawk colonies.
One of nature’s patterns connects the percent of adult birds in a
colony that return from the previous year and the number of new adults that join the colony. Can the
percent of returning adult birds be use to predict the number of new adults that join the colony?
a.
Is this an experiment or an observational study? Can we conclude causation?
Observational study—cannot conclude causation
b.
What are the explanatory and response variables? What type of variable are they?
Explanatory variable: Percent of adult birds returning
Response variable: Number of new adults that join the colony
c.
What statistical procedure should be performed to answer the research question?
Regression analysis since the data are bivariate quantitative—two different measurements on
each individual.
d.
State the hypotheses in words and in symbols for testing whether a linear relationship exists
between the two variables “Percent return” and “new birds”.
H
0
: percent of returning adult birds cannot be used to predict number of new adult birds.
H
a
: percent of returning adult birds can be used to predict number of new adult birds.
H
0
:
β
= 0
versus
H
a
:
≠
0
e.
Is the condition of equal variance met? Why or why not?
Yes—no megaphone in residual plot
Is the condition of linear relationship met? Why or why not?
Yes—no smile or frown in residual
plot
Is the condition of Normality of residuals met? Why or why not?
Yes—no outliers or strong
skewness in dotplot of residuals so t distribution is robust with respect to Normality
Is it reasonable to assume that the 13 colonies are independent of each other? Why?
Yes—no reason
to suspect that birds in one colony interact with birds in another colony.
f.
Using the regression printout, what are the values of the t test statistic and
P
value for testing
H
0
: β
= 0
(slope)?
On second row of computer output:
t
=
3.7432015
and Pvalue =
0.0032
g.
At
α
= 0.05 what can you conclusions can you make about whether we can use the percentage of
returning birds to predict the number of new adult birds?
Since Pvalue <
α
, we reject H
0
and conclude that the percentage of returning birds can be used
to predict the number of new birds.
h.
Interpret slope in context.
For every one percent increase in percent of returning birds, there is an average decrease of 0.3
new adult birds.
i.
What is a 95% confidence interval for β
(slope)?
df = n – 2 = 13 – 2 = 11
t
* = 2.201 for 95% confidence
b = 0.304
SE
b
= 0.081
95% confidence interval for b is: 0.304 ± (2.201) ( 0.081) or (0.482, 0.126)
Note: values for b and SE
b
are found on the bottom row of the regression output.
j.
Interpret r
2
in context.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document56% of the variation in new adult birds joining the colony can be explained by the
percent of returning adult birds.
k.
What is the predicted number of new adult birds in a colony when 60% of the birds return?
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 Collings
 Normal Distribution, new adult birds

Click to edit the document details