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Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2?
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Obtain two regression equations by the method of least square from the...
Regression Equations by the Method of Least Squares
Data:
- x: 8 6 4 7 5
- y: 9 8 5 6 2
Explanation:
Regression analysis is used to determine the relationship between a dependent variable and one or more independent variables. The method of least squares is a statistical technique used to find the line of best fit for a set of data. In this method, the sum of the squares of the vertical distances between each data point and the line of best fit is minimized.
Regression Equation for y on x:
The regression equation for y on x is used to predict the value of y for a given value of x. It is represented as:
y = a + bx
- a: y-intercept
- b: slope of the line
Step 1: Calculate the mean of x and y
- Mean of x = (8+6+4+7+5)/5 = 6
- Mean of y = (9+8+5+6+2)/5 = 6
Step 2: Calculate the slope (b)
b = Σ[(x - x̄)(y - ȳ)] / Σ[(x - x̄)²]
- Σ[(x - x̄)(y - ȳ)] = (8-6)(9-6) + (6-6)(8-6) + (4-6)(5-6) + (7-6)(6-6) + (5-6)(2-6) = -2+0-2+0-4 = -8
- Σ[(x - x̄)²] = (8-6)² + (6-6)² + (4-6)² + (7-6)² + (5-6)² = 4+0+4+1+1 = 10
- b = -8/10 = -0.8
Step 3: Calculate the y-intercept (a)
a = ȳ - bx̄
- a = 6 - (-0.8)(6) = 10.8
Step 4: Write the regression equation for y on x
y = 10.8 - 0.8x
Regression Equation for x on y:
The regression equation for x on y is used to predict the value of x for a given value of y. It is represented as:
x = a' + b'y
- a': x-intercept
- b': slope of the line
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Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2?
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Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2?.
Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2? for B Com 2025 is part of B Com preparation. The Question and answers have been prepared according to the B Com exam syllabus. Information about Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2? covers all topics & solutions for B Com 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Obtain two regression equations by the method of least square from the following data : x : 8 6 4 7 5 y : 9 8 5 6 2?.
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