Question

In: Statistics and Probability

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 data are given in tabular form and also displayed in the Figure 1 scatter plot, which gives the least-squares regression line as well. The equation for this line is =y+88.570.52x

.

Height of father, x
(in centimeters)		 Height of son, y
(in centimeters)
160.6 170.6
181.9 179.2
190.0 195.4
175.1 179.5
162.4 167.9
201.7 190.5
184.5 189.0
157.2 174.9
173.8 170.7
182.0 188.3
172.4 182.3
200.4 190.7
193.6 188.9
176.7 174.5
190.1 188.7
187.9 176.2
      

x

150

160

170

180

190

200

210

y

150

160

170

180

190

200

210

0
Figure 1

Answer the following:

1. Fill in the blank: For these data, heights of sons that are greater than the mean of the heights of sons tend to be paired with heights of fathers that are _____ the mean of the heights of fathers. Choose onegreater thanless than
2. According to the regression equation, for an increase of one centimeter in father's height, there is a corresponding increase of how many centimeters in son's height?
3. From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 187.9 centimeters? (Round your answer to at least one decimal place.)
4. What was the observed son's height (in centimeters) when the height of the father was 187.9 centimeters?

Solutions

Expert Solution

The dependent variable 'y' is the son's height and the independent variable 'x' is the fther's height. We use regression to predict 'y' based on 'x'.

The regression equation is given by

Where the slope = 0.52

Slope =

intercept = 88.57

intercept =

1. Fill in the blank: For these data, heights of sons that are greater than the mean of the heights of sons tend to be paired with heights of fathers that are _____ the mean of the heights of fathers.

Exp: Since the slope is positive, we can say that 'y' would increase with an increase in 'x'. There is positive correlation, therefore both will be greater if one is greater than the mean and vice versa.

 Greater than

2. According to the regression equation, for an increase of one centimeter in father's height, there is a corresponding increase of how many centimeters in son's height?

Exp: Slope determines the magnitude of change in 'y' due to a change in 'x'.

 0.52

3. From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 187.9 centimeters? (Round your answer to at least one decimal place.)

Exp: Simply sub x = 187.9 in the regression equation since it says prediction.

 185.448

4. What was the observed son's height (in centimeters) when the height of the father was 187.9 centimeters?

Exp: It says 'pbserved' means the height that is recorded and present in the data.

 176.2

orchestra answered 2 years ago
Next > < Previous

Related Solutions

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...
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...
How did child labor of the late 1800s and late 1900s affect society?
How did child labor of the late 1800s and late 1900s affect society?
UNITE is a union that was established in the late 1800s to represent workers in the...
UNITE is a union that was established in the late 1800s to represent workers in the hospitality industry, including restaurants, hotels, foodservice, and gaming organizations. The union is very active in gay, lesbian, and transgender issues. Employees enjoy the protections that are offered by working at a unionized establishment, however they are concerned about rights to privacy as they relate to mandatory testing in the workplace. If a company follows the progressive discipline rule, what type of discipline should be...
UNITE is a union that was established in the late 1800s to represent workers in the...
UNITE is a union that was established in the late 1800s to represent workers in the hospitality industry, including restaurants, hotels, foodservice, and gaming organizations. The union is very active in gay, lesbian, and transgender issues. Employees enjoy the protections that are offered by working at a unionized establishment, however they are concerned about rights to privacy as they relate to mandatory testing in the workplace. UNITE’S vice president explains that under the law, employees can get fired for any...
UNITE is a union that was established in the late 1800s to represent workers in the...
UNITE is a union that was established in the late 1800s to represent workers in the hospitality industry, including restaurants, hotels, foodservice, and gaming organizations. The union is very active in gay, lesbian, and transgender issues. Employees enjoy the protections that are offered by working at a unionized establishment, however they are concerned about rights to privacy as they relate to mandatory testing in the workplace. In practicing progressive discipline, all of the following are acceptable disciplinary actions that may...
UNITE is a union that was established in the late 1800s to represent workers in the...
UNITE is a union that was established in the late 1800s to represent workers in the hospitality industry, including restaurants, hotels, foodservice, and gaming organizations. The union is very active in gay, lesbian, and transgender issues. Employees enjoy the protections that are offered by working at a unionized establishment, however they are concerned about rights to privacy as they relate to mandatory testing in the workplace. It is recommended that unionized organizations use approaches to discipline that include the elements...
A fundamental assumption of administrative reformers in the late 1800s and early 1900s was that politics...
A fundamental assumption of administrative reformers in the late 1800s and early 1900s was that politics could have only adverse affects on administration. How valid is that belief? How, and to what extent, do current administrative structures and practices reflect that assumption? And do you see politics as a contructive force in governance?
Various reform groups with various causes developed in the US in the late 1800s and early...
Various reform groups with various causes developed in the US in the late 1800s and early 1900s; these are loosely called “Progressives” as they aimed to use government policies or science to improve and advance society. Also, this period was a time when the US started as a major player in international conflicts—first in the “Spanish American War and then in World War I. There were deep isolationist sentiments about such overseas entanglements, and President Wilson first has one position...
Various reform groups with various causes developed in the US in the late 1800s and 1900s;...
Various reform groups with various causes developed in the US in the late 1800s and 1900s; these are loosley called "Progressives" as they aimed to use government policies or science to improve and advanve society. Also, this period was a time when the US started as a major player in inernational conflicts-first in the "Spanish American War and then in World War 1. There were deep isolationist sentiments about such overseas entanglements, and President Wilson first has one position and...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT