Question
In: Statistics and Probability
Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children...
Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19th century. It is from this study that the name "regression" originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship:
studenth = 19.6 + 0.73 × Midparh, R2 = 0.45, SER = 2.0
(7.2) (0.10)
where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton's methodology, both variables were adjusted so that the average female height was equal to the average male height.)
(a) Test for the statistical significance of the slope coefficient.
(b) If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept. Test the hypothesis.
(i) Can you reject the null hypothesis that the regression R^2 is zero?
(ii) Construct a 95% confidence interval for a one inch increase in the average of parental height.
Solutions
orchestra answered 2 years agoRelated Solutions
Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of...
Sir Francis Galton, in the late 1800s, was the first to
introduce the statistical concepts of regression and correlation.
He studied the relationships between pairs of variables such as the
size of parents and the size of their offspring.
Data similar to that which he studied are given below, with the
variable x denoting the height (in centimeters) of a human father
and the variable y denoting the height at maturity (in centimeters)
of the father's oldest (adult) son. The...
From the time of early studies by Sir Francis Galton in the late nineteenth century linking...
From the time of early studies by Sir Francis Galton in the late
nineteenth century linking it with mental ability, the cranial
capacity of the human skull has played an important role in
arguments about IQ, racial differences, and evolution, sometimes
with serious consequences. (See, for example, S.J. Gould, "The
Mismeasure of Man," .) Suppose that the mean cranial capacity
measurement for modern, adult males is cc (cubic centimeters) and
that the standard deviation is cc. Complete the following
statements...
We are studying the relationship of age in years and height in inches for children of...
We are studying the relationship of age in years and height in
inches for children of ages from 2 - 10. We have a sample of five
children. It is a linear relationship, so please find:
(a) r
(b) r(sq);
(c) the equation of the regression line
(d) the expected height in inches for a 7 year-old child.
Age(X)
Height(Y)
2
37
3
40
3
42
6
47
9
54
Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number...
Mr. James, president of Daniel-James Financial Services,
believes that there is a relationship between the number of client
contacts and the dollar amount
of sales. To document this assertion, he gathered the following
information from a sample of clients for the last month. Let X
represent the number of times that the client was contacted and Y
represent the value of sales ($1000) for each client sampled.
Number
of`
Sales
Contacts
(X)
($1000) (Y)
14
24
...
Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number...
Mr. James, president of Daniel-James Financial Services,
believes that there is a relationship between the number of client
contacts and the dollar amount of sales. To document this
assertion, he gathered the following information from a sample of
clients for the last month. Let X represent the number of times
that the client was contacted and Y represent the value of sales
($1000) for each client sampled.
Number
of`
Sales
Contacts
(X)
($1000)
10 26
8 21
12...
Mr. James, president of Daniel-James Financial Services, believes that there is a relationship between the number...
Mr. James, president of Daniel-James Financial Services,
believes that there is a relationship between the number of client
contacts and the dollar amount of sales. To document this
assertion, he gathered the following information from a sample of
clients for the last month. Let X represent the number of times
that the client was contacted and Y represent the value of sales
($1000) for each client sampled.
Number
of`
Sales
Contacts
(X)
($1000)
10 26
8 21
12...
Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number...
Mr. James McWhinney, president of Daniel-James Financial
Services, believes there is a relationship between the number of
client contacts and the dollar amount of sales. To document this
assertion, Mr. McWhinney gathered the following sample information.
The x column indicates the number of client contacts last month and
the y column shows the value of sales ($ thousands) last month for
each client sampled.
Number of Contacts,X
Sales ($ thousands),y
Number of Contacts,x
Sales ($ thousands),y
14
24
23
30...
Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number...
Mr. James McWhinney, president of Daniel-James Financial
Services, believes there is a relationship between the number of
client contacts and the dollar amount of sales. To document this
assertion, Mr. McWhinney gathered the following sample information.
The X column indicates the number of client contacts last month,
and the Y column shows the value of sales ($ thousands) last month
for each client sampled.
Number of Contacts (X)
Sales ($ thousands) (Y)
14
24
12
14
20
28
16
30...
A cross-sectional study examined children between the ages of 1 and 17 to determine the prevalence...
A cross-sectional study examined children
between the ages of 1 and 17 to determine the prevalence of asthma
and of indoor environmental risk factors for childhood asthma. Data
was collected by questionnaires, which were completed by each
child's primary caretaker. Having a smoker in the household was
found to be a significant risk factor for childhood asthma. The
following 2X2 table illustrates the study findings related to this
risk factor.
Outcome
Exposure
Asthma
No Asthma
Total
Smoker in the household...
An epidemiologic study in Belgium examined the relationship between daily sunlight exposure and the development of...
An epidemiologic study in Belgium examined the relationship
between daily sunlight exposure and the development of cataracts in
8,000 individuals. The results of the study were as follows: OR =
1.9 (95% CI = 1.2 to 4.6). After controlling for vitamin E intake,
a possible protective factor, the ORMH was 3.6 (95% CI = 1.3 to
5.1). Failure to control for Viramin E led to which of the
following in the above study?
A. Negative Confounding
B. Selection Bias
C....
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