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How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)?
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How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and s...
Shifting the Origin and Changing the Scale of X in a Trend Equation
When a trend equation is given as Y = 80 + 4X + 1.6X^2 with origin: 1978 and scale: 1 unit of X = 1 year, it means that the dependent variable Y is a function of the independent variable X. The equation can be used to predict the value of Y for any given value of X.
To change the origin and scale of X, we need to follow the steps below:
Step 1: Shift the origin forward by 2 years.
To shift the origin forward by 2 years, we need to subtract 2 from the value of X. This is because the value of X represents the number of years from the original origin (1978). So, if we subtract 2 from X, we are effectively shifting the origin forward by 2 years.
The new equation becomes Y = 80 + 4(X-2) + 1.6(X-2)^2.
Step 2: Change the scale of X to half-yearly units.
To change the scale of X to half-yearly units, we need to divide the value of X by 2. This is because 1 unit of X now represents ½ year instead of 1 year.
The new equation becomes Y = 80 + 4(X/2-1) + 1.6(X/2-1)^2.
Step 3: Simplify the equation.
We can simplify the equation by expanding the square term and collecting like terms.
The new equation becomes Y = 47.2 + 2.6X + 0.2X^2.
Therefore, the new trend equation with shifted origin and changed scale of X is Y = 47.2 + 2.6X + 0.2X^2.
When a trend equation is given as Y = 80 + 4X + 1.6X^2 with origin: 1978 and scale: 1 unit of X = 1 year, it means that the dependent variable Y is a function of the independent variable X. The equation can be used to predict the value of Y for any given value of X.
To change the origin and scale of X, we need to follow the steps below:
Step 1: Shift the origin forward by 2 years.
To shift the origin forward by 2 years, we need to subtract 2 from the value of X. This is because the value of X represents the number of years from the original origin (1978). So, if we subtract 2 from X, we are effectively shifting the origin forward by 2 years.
The new equation becomes Y = 80 + 4(X-2) + 1.6(X-2)^2.
Step 2: Change the scale of X to half-yearly units.
To change the scale of X to half-yearly units, we need to divide the value of X by 2. This is because 1 unit of X now represents ½ year instead of 1 year.
The new equation becomes Y = 80 + 4(X/2-1) + 1.6(X/2-1)^2.
Step 3: Simplify the equation.
We can simplify the equation by expanding the square term and collecting like terms.
The new equation becomes Y = 47.2 + 2.6X + 0.2X^2.
Therefore, the new trend equation with shifted origin and changed scale of X is Y = 47.2 + 2.6X + 0.2X^2.
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How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)?
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How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)? 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 How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)?.
How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)? 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 How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How would the trend equation Y 80+ 4X+ 1.6x^2 (with origin: 1978 and scale: 1 unit of X-1 year) change if origin is shifted forward by 2 years and the scale of X is changed to half-yearly units i.e., I unit of X = ½ years. (Ans: 47.2 +2.6x +0.2x^2)?.
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