Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > For a bivariate data set on (x, y), if the me...
Start Learning for Free
For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient are
x̅ = 1.0, y̅ = 2.0, sx = 3.0, sy = 9.0, r = 0.8
Then the regression line of y on x is:
x̅ = 1.0, y̅ = 2.0, sx = 3.0, sy = 9.0, r = 0.8
Then the regression line of y on x is:
- a)y = 1 + 2.4(x - 1)
- b)y = 2 + 0.27(x - 1)
- c)y = 2 + 2.4(x - 1)
- d)y = 1 + 0.27(x - 2)
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
For a bivariate data set on (x, y), if the means, standard deviations ...
Formula
The regression line of y on x is given as
y - y̅ = r × σy(x - x̅)/σx
Calculation
According to the question
y - 2 = 0.8 × 9(x - 1)/3
⇒ y - 2 = 2.4(x - 1)
∴ y = 2 + 2.4(x - 1)
Free Test
FREE
| Start Free Test |
Community Answer
For a bivariate data set on (x, y), if the means, standard deviations ...
Given:
The means of x and y: x = 1.0, y = 2.0
The standard deviations of x and y: sx = 3.0, sy = 9.0
The correlation coefficient: r = 0.8
Explanation:
The regression line of y on x represents the line that best fits the data points in the scatter plot of x and y. This line can be expressed in the form of y = a + bx, where a is the y-intercept and b is the slope of the line.
Step 1: Calculate the slope (b) of the regression line:
The slope of the regression line can be calculated using the formula:
b = r * (sy / sx)
Given that r = 0.8, sy = 9.0, and sx = 3.0, we can substitute these values into the formula to find b:
b = 0.8 * (9.0 / 3.0) = 0.8 * 3.0 = 2.4
Therefore, the slope of the regression line is 2.4.
Step 2: Calculate the y-intercept (a) of the regression line:
The y-intercept of the regression line can be calculated using the formula:
a = y - b * x
Given that x = 1.0, y = 2.0, and b = 2.4, we can substitute these values into the formula to find a:
a = 2.0 - 2.4 * 1.0 = 2.0 - 2.4 = -0.4
Therefore, the y-intercept of the regression line is -0.4.
Step 3: Write the equation of the regression line:
Now that we have the slope (b = 2.4) and the y-intercept (a = -0.4), we can write the equation of the regression line:
y = -0.4 + 2.4x
Simplifying the equation, we get:
y = 2.4x - 0.4
Comparing this equation with the given options, we can see that the correct answer is option 'C':
y = 2.4(x - 1)
This equation represents the regression line of y on x for the given bivariate data set.
The means of x and y: x = 1.0, y = 2.0
The standard deviations of x and y: sx = 3.0, sy = 9.0
The correlation coefficient: r = 0.8
Explanation:
The regression line of y on x represents the line that best fits the data points in the scatter plot of x and y. This line can be expressed in the form of y = a + bx, where a is the y-intercept and b is the slope of the line.
Step 1: Calculate the slope (b) of the regression line:
The slope of the regression line can be calculated using the formula:
b = r * (sy / sx)
Given that r = 0.8, sy = 9.0, and sx = 3.0, we can substitute these values into the formula to find b:
b = 0.8 * (9.0 / 3.0) = 0.8 * 3.0 = 2.4
Therefore, the slope of the regression line is 2.4.
Step 2: Calculate the y-intercept (a) of the regression line:
The y-intercept of the regression line can be calculated using the formula:
a = y - b * x
Given that x = 1.0, y = 2.0, and b = 2.4, we can substitute these values into the formula to find a:
a = 2.0 - 2.4 * 1.0 = 2.0 - 2.4 = -0.4
Therefore, the y-intercept of the regression line is -0.4.
Step 3: Write the equation of the regression line:
Now that we have the slope (b = 2.4) and the y-intercept (a = -0.4), we can write the equation of the regression line:
y = -0.4 + 2.4x
Simplifying the equation, we get:
y = 2.4x - 0.4
Comparing this equation with the given options, we can see that the correct answer is option 'C':
y = 2.4(x - 1)
This equation represents the regression line of y on x for the given bivariate data set.
Attention Civil Engineering (CE) Students!
To make sure you are not studying endlessly, EduRev has designed Civil Engineering (CE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Civil Engineering (CE).
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer?
Question Description
For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer?.
For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer?.
Solutions for For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer?, a detailed solution for For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For a bivariate data set on (x, y), if the means, standard deviations and correlation coefficient arex = 1.0, y = 2.0, sx= 3.0, sy= 9.0, r = 0.8Then the regression line of y on x is:a)y = 1 + 2.4(x - 1)b)y = 2 + 0.27(x - 1)c)y = 2 + 2.4(x - 1)d)y = 1 + 0.27(x - 2)Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup