Malaika Wauters Math 11 - Lab 8
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Course
11
Subject
Mathematics
Date
May 30, 2024
Type
Pages
5
Uploaded by MegaRose1330
Malaika Wauters
Math 11
Denise Rava
Lab 8: Predicting Children’s Growth
1.
Begin by using linear regression to predict a child's height at age 9 from the child's height
at age 2. What is the equation of your regression line? Based on your scatter plot and
residual plot, does linear regression seem like an appropriate way to predict heights?
a.
Equation of regression line: HT9 = 31.93 + 1.796(HT2)
b.
Based on my scatter and residual plot above, I would suggest that linear
regression is appropriate to predict heights because there is an absence of any
curvature, heteroskedasticity in the residual plot and the points seem relatively
randomly scattered.
2.
Next try using linear regression to predict a child's height at age 18 from the child's
height at age 9. What is the equation of your regression line? Does linear regression seem
appropriate for these data?
a.
Equation of regression line: HT18 = 32.2 + 1.035(HT9)
b.
Analyzing the scatter and residual plots depicted above, linear regression once
again seems like an appropriate model to predict the heights of children at age 18.
There is no heteroskedasticity or curvature in the residual plot and moreover, the
data seems to be randomly scattered.
3.
Is there a big difference between how much boys and girls grow in height between age 2
and age 9, or does the regression line you found in question 1 appear to work pretty well
for both boys and girls?
a. Evidently, the scatter plot on the left
demonstrates that the regression line from
question 1 can apply and work well for
both boys and girls, the slopes are very
similar, the female slope is just ever so
slightly steeper than the male height slope.
4.
Now consider the period between age 9 and age 18. Is there a big difference between the
growth patterns of boys and girls in height during this period, or does the regression line
you found in question 2 work well for both boys and girls?
a. Unfortunately the regression line found
as a result of question 1 does not seem to
work well for the heights of 18 year old
boys and girls because the regression lines
for the boys and girls on this scatterplot
have different slopes and y intercepts.
5.
Find the equation of a regression line that can be used to predict a boy's height at age 18
from the boy's height at age 9.
a.
HT18 = 35.08 + 1.059(HT9)
6.
What percentage of the variation in the boys' heights at age 18 is explained by this
regression.
a.
R^2 = 76.54%
7.
Are the assumptions required for statistical inference satisfied? Explain how you arrive at
your conclusions and provide supporting plots.
a.
The plot seems to be linear and the data points
show linear assumption, the randomness of the
plot points also show that the independence
assumption is met, and the equal variance
assumption is met clearly with the even random
scatter of plots on the residual plot. Since the
sample size is greater than 30, the central limit
theorem suggests that the normal assumption is met. Therefore, the assumptions
for statistical inference are satisfied.
8.
Can you conclude that there is an association between boys' heights at age 18 and their
heights at age 9? Make sure to state your null and alternative hypotheses and give the
T-statistic and p-value for your test. Use significance level .05.
a.
H
0
: b
1
=0
H
A
: b
1
≠0
T-value = 14.45
P-value = 0
b.
Since the p-value is less than 0.05, we reject the null hypothesis that states that
there is not an association between heights at age 9 and 18 for boys, and thus, we
can conclude that there is an association between the heights because there is
statistically sufficient evidence.
9.
Find a 95 percent confidence interval for the slope of your regression line. Explain
carefully in a sentence or two what this confidence interval means.
a.
D.f = n - 2 = 64
b.
ME = (1.9975)(0.07328) = 0.146
c.
95% confidence interval is b
1
+/- ME = (0.913, 1.21)
d.
The confidence interval tells us that we can be 95% confident that there is a 1 cm
increase in height at 9 years old associated with an increase in height at age 18 on
average between the above interval.
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