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Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d then
- a)The two fitted lines must coincide
- b)The two fitted lines need not coincide
- c)It is possible that ac = 0
- d)A must be 1/c
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in t...
y = ax + b -(i) and x = cy + d - (ii)
From (ii) wee get x - d = cy ⇒ y = 1/c x - d/c - (iii)
comparing (i) and (ii), a = 1/c and b = -d/c
From (ii) wee get x - d = cy ⇒ y = 1/c x - d/c - (iii)
comparing (i) and (ii), a = 1/c and b = -d/c
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Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in t...
Explanation:
To understand why option D is the correct answer, let's analyze the given information and use the method of least squares to find the regression lines.
1. Fitted line y = ax + b:
We are given that the fitted line when regressing y upon x is given by y = ax + b. This means that we are trying to find a linear relationship between the variables x and y, where a is the slope of the line and b is the y-intercept.
2. Fitted line x = cy + d:
We are also given that the fitted line when regressing x upon y is given by x = cy + d. In this case, we are trying to find a linear relationship between the variables y and x, where c is the slope of the line and d is the y-intercept.
Now, let's consider the relationship between these two lines:
- The slope of the first line, y = ax + b, is a.
- The slope of the second line, x = cy + d, is 1/c.
Since we are given that a is the slope of the first line, and the slope of the second line is 1/c, we can conclude that a must be equal to 1/c. Therefore, option D is correct.
Summary:
Based on the given information and the method of least squares, we can conclude that the slope of the fitted line when regressing y upon x (a) is equal to the reciprocal of the slope of the fitted line when regressing x upon y (1/c), which is represented by option D.
To understand why option D is the correct answer, let's analyze the given information and use the method of least squares to find the regression lines.
1. Fitted line y = ax + b:
We are given that the fitted line when regressing y upon x is given by y = ax + b. This means that we are trying to find a linear relationship between the variables x and y, where a is the slope of the line and b is the y-intercept.
2. Fitted line x = cy + d:
We are also given that the fitted line when regressing x upon y is given by x = cy + d. In this case, we are trying to find a linear relationship between the variables y and x, where c is the slope of the line and d is the y-intercept.
Now, let's consider the relationship between these two lines:
- The slope of the first line, y = ax + b, is a.
- The slope of the second line, x = cy + d, is 1/c.
Since we are given that a is the slope of the first line, and the slope of the second line is 1/c, we can conclude that a must be equal to 1/c. Therefore, option D is correct.
Summary:
Based on the given information and the method of least squares, we can conclude that the slope of the fitted line when regressing y upon x (a) is equal to the reciprocal of the slope of the fitted line when regressing x upon y (1/c), which is represented by option D.
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Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer?
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Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer?.
Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four arbitrary point (x1,y1), (x2,y2),(x3,y3), (x4,y4), are given in the x, y - Plane Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x given the fitted line x = cy + d thena)The two fitted lines must coincideb)The two fitted lines need not coincidec)It is possible that ac = 0d)A must be 1/cCorrect answer is option 'D'. Can you explain this answer?.
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