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The following data relate to the heights of 10 pairs of fathers and sons:
(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)
Q. The regression equation of height of son on that of father is given by
- a)y = 100 + 5x
- b)y = 99.708 + 0.405x
- c)y = 89.653 + 0.582x
- d)y = 88.758 + 0.562x
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The following data relate to the heights of 10 pairs of fathers and so...
Regression Analysis:
Regression analysis is a statistical method to determine the relationship between two or more variables. It is used to find the relationship between a dependent variable (y) and one or more independent variables (x1, x2, …, xn).
In this question, we need to find the regression equation of the height of the son on that of the father.
Data Given:
The following data relate to the heights of 10 pairs of fathers and sons:
(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175), (169, 170), (170, 173)
Calculations:
- Calculate the mean of the heights of fathers (x̄) and the mean of the heights of sons (ȳ).
- Calculate the deviations of the heights of fathers (xi) and the heights of sons (yi) from their respective means.
- Calculate the sum of the products of the deviations of the heights of fathers and sons.
- Calculate the sum of the squares of the deviations of the heights of fathers.
- Calculate the slope (b) of the regression equation using the formula:
b = Σ(xi * yi) / Σ(xi^2)
- Calculate the intercept (a) of the regression equation using the formula:
a = ȳ - b * x̄
- The regression equation of the height of son on that of father is given by:
y = a + bx
where y is the height of the son and x is the height of the father.
Solution:
- Mean of the heights of fathers (x̄) = (175 + 172 + 167 + 168 + 172 + 171 + 174 + 176 + 169 + 170) / 10 = 171.4
- Mean of the heights of sons (ȳ) = (173 + 172 + 171 + 171 + 173 + 170 + 173 + 175 + 170 + 173) / 10 = 172.1
- Deviations of the heights of fathers (xi) = (175 - 171.4), (172 - 171.4), (167 - 171.4), (168 - 171.4), (172 - 171.4), (171 - 171.4), (174 - 171.4), (176 - 171.4), (169 - 171.4), (170 - 171.4) = 3.6, 0.6, -4.4, -3.4, 0.6, -0.4, 2.6, 4.6, -2.4, -1.4
- Deviations of the heights of sons (yi) = (173 - 172.1), (172 - 172.1), (171 - 172.1), (171 - 172.1), (173 - 172.1), (170 - 172.1), (173 - 172.1), (175 - 172.1), (170 - 172.1), (173 - 172.1) = 0.9, -0.1, -1.1, -1.1,
Regression analysis is a statistical method to determine the relationship between two or more variables. It is used to find the relationship between a dependent variable (y) and one or more independent variables (x1, x2, …, xn).
In this question, we need to find the regression equation of the height of the son on that of the father.
Data Given:
The following data relate to the heights of 10 pairs of fathers and sons:
(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175), (169, 170), (170, 173)
Calculations:
- Calculate the mean of the heights of fathers (x̄) and the mean of the heights of sons (ȳ).
- Calculate the deviations of the heights of fathers (xi) and the heights of sons (yi) from their respective means.
- Calculate the sum of the products of the deviations of the heights of fathers and sons.
- Calculate the sum of the squares of the deviations of the heights of fathers.
- Calculate the slope (b) of the regression equation using the formula:
b = Σ(xi * yi) / Σ(xi^2)
- Calculate the intercept (a) of the regression equation using the formula:
a = ȳ - b * x̄
- The regression equation of the height of son on that of father is given by:
y = a + bx
where y is the height of the son and x is the height of the father.
Solution:
- Mean of the heights of fathers (x̄) = (175 + 172 + 167 + 168 + 172 + 171 + 174 + 176 + 169 + 170) / 10 = 171.4
- Mean of the heights of sons (ȳ) = (173 + 172 + 171 + 171 + 173 + 170 + 173 + 175 + 170 + 173) / 10 = 172.1
- Deviations of the heights of fathers (xi) = (175 - 171.4), (172 - 171.4), (167 - 171.4), (168 - 171.4), (172 - 171.4), (171 - 171.4), (174 - 171.4), (176 - 171.4), (169 - 171.4), (170 - 171.4) = 3.6, 0.6, -4.4, -3.4, 0.6, -0.4, 2.6, 4.6, -2.4, -1.4
- Deviations of the heights of sons (yi) = (173 - 172.1), (172 - 172.1), (171 - 172.1), (171 - 172.1), (173 - 172.1), (170 - 172.1), (173 - 172.1), (175 - 172.1), (170 - 172.1), (173 - 172.1) = 0.9, -0.1, -1.1, -1.1,
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The following data relate to the heights of 10 pairs of fathers and so...
The regression equation of height of son on that of the father is Y= 0.44X-96.684Y=0.44X−96.684 .
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The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer?
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The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer?.
The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The following data relate to the heights of 10 pairs of fathers and sons:(175, 173), (172, 172), (167, 171), (168, 171), (172, 173), (171, 170), (174, 173), (176, 175) (169, 170), (170, 173)Q. The regression equation of height of son on that of father is given bya)y = 100 + 5xb)y = 99.708 + 0.405xc)y = 89.653 + 0.582xd)y = 88.758 + 0.562xCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
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