Sir Francis Galton, in the late 1800 s, 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 scatter plot below, which gives the least-squares regression line as well. The equation for this line is y =95.35 +0.48 x. Height of Height of son, father, x (in centimeters) centimeters) y (in 175.8 178.1 193.5 190.3 210. 183.2 176.6 173.3 171.1 200- 183.8 186.5 190. 175.8 175.6 180- 159.8 167.2 170 155.5 175.8 162.0 172.1 160- 190.9 188.0 150 180.1 187.1 180 190 200 210 186.9 177.5 171.5 181.5 Height of father, x (in centimeters) 190.5 195.7 201.0 189.9 204.2 191.0 Send data to calculator Send data to Excel Based on the sample data and the regression line, complete the following. |(a) For these data, heights of fathers that are less than the mean of the heights of fathers tend to be paired with heights of sons that are ((Choose one) V the mean of the heights sons. greater than less than (b) 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? (c) From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 171.5 centimeters? (Round your answer to at least one decimal place.) (d) What was the observed son's height (in centimeters) when the height of the father was 171.5 centimeters? (in centimeters) 'uos jo aubiƏH
Sir Francis Galton, in the late 1800 s, 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 scatter plot below, which gives the least-squares regression line as well. The equation for this line is y =95.35 +0.48 x. Height of Height of son, father, x (in centimeters) centimeters) y (in 175.8 178.1 193.5 190.3 210. 183.2 176.6 173.3 171.1 200- 183.8 186.5 190. 175.8 175.6 180- 159.8 167.2 170 155.5 175.8 162.0 172.1 160- 190.9 188.0 150 180.1 187.1 180 190 200 210 186.9 177.5 171.5 181.5 Height of father, x (in centimeters) 190.5 195.7 201.0 189.9 204.2 191.0 Send data to calculator Send data to Excel Based on the sample data and the regression line, complete the following. |(a) For these data, heights of fathers that are less than the mean of the heights of fathers tend to be paired with heights of sons that are ((Choose one) V the mean of the heights sons. greater than less than (b) 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? (c) From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 171.5 centimeters? (Round your answer to at least one decimal place.) (d) What was the observed son's height (in centimeters) when the height of the father was 171.5 centimeters? (in centimeters) 'uos jo aubiƏH
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Transcribed Image Text:Sir Francis Galton, in the late 1800 s, 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 scatter plot below, which gives
the least-squares regression line as well. The equation for this line is y =95.35 +0.48 x
Height of
Height of son,
father, x
(in
centimeters) centimeters)
y
(in
175.8
178.1
193.5
190.3
210.
183.2
176.6
173.3
171.1
200-
183.8
186.5
190.
175.8
175.6
180
159.8
167.2
xx
170
155.5
175.8
162.0
172.1
160-
190.9
188.0
150
180.1
187.1
Tdo ito Ido 130 200 z1o
186.9
177.5
171.5
181.5
Height of father, x
(in centimeters)
190.5
195.7
201.0
189.9
204.2
191.0
Send data to calculator
Send data to Excel
Based on the sample data and the regression line, complete the following.
(a) For these data, heights of fathers that are less than the mean of the heights of fathers tend to be paired with heights of
sons that are ((Choose one) V the mean of the heights of sons.
greater than
less than
(b) 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?
(c) From the regression equation, what is the predicted son's height (in centimeters) when the height of the father is 171.5
centimeters? (Round your answer to at least one decimal place.)
(d) What was the observed son's height (in centimeters) when the height of the father was 171.5 centimeters?
Height of son, y
(in centimeters)
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