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Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by?
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Following are the two normal equations obtained for deriving the regre...
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We need to solve the two normal equations to get the value of 'a' (y intercept) & 'b' (slope) of the regression line y on x.
5a + 10b = 40 Multiply the eqn. by 2 & solve
10a + 25b = 95
10a + 20b = 80
so 'b' = 3 & 'a' = 2
The equation would be Y = 2 + 3X
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Following are the two normal equations obtained for deriving the regre...
Regression Line of Y on X
Normal Equations
- 5a + 10b = 40
- 10a + 25b = 95
Solving for a and b
To solve for the coefficients a and b of the regression line of Y on X, we need to solve the normal equations simultaneously. We can use any method of solving systems of linear equations, such as substitution or elimination. Here, we will use elimination:
- Multiplying the first equation by -2, we get: -10a - 20b = -80
- Adding this to the second equation, we get: 0a + 5b = 15
- Dividing by 5, we get: b = 3
- Substituting this value of b into the first equation, we get: 5a + 10(3) = 40
- Solving for a, we get: a = 2
Regression Line Equation
Now that we have found the values of a and b, we can write the equation for the regression line of Y on X:
Y = a + bX
Y = 2 + 3X
Interpretation
This equation means that for every one unit increase in X, we can expect Y to increase by 3 units. The intercept of 2 means that when X is zero, the predicted value of Y is 2.
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Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by?
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Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by?.
Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Following are the two normal equations obtained for deriving the regression line of Y and x: 5a 10b=40 10a 25b=95 The regression line of Y on X is given by?.
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