In econometrics, when working with regression analysis, the summation of xi² in raw form can be calculated from its deviation form using the formula: Σxi² = Σ(xi - x̄)² + n(x̄)², where n is the sample size and x̄ is the mean of x. Given the deviation form value of Σ(xi - x̄)² = 116, n = 7, and x̄n = 81, the raw form Σxi² equals 683. This value is then used to calculate the standard error of beta1, which comes out to be 0.2282.
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Sem 4 Introductory Econometrics PYQ | 2025 PYQ Question 7 | BA (H) Economics | Delhi University | P4Added:
Come on son, now let us learn how to go ahead and find summation xi² in its raw form.
So, the formula that we are using is this.
Now ma'am, how is this formula coming? How is this formula coming? So it is very simple.
We know that when we write in deviation form, the summation xi, if I write it in a very simple form, then our xi in deviation form is capital xi - x times. And now if I want to square these on both sides then I can square them here. And here I can make a submission.
Here I can put a submission with it.
So as soon as I do this and rewrite it, after opening it, this formula will appear to us. So now our formula becomes summation xi² = xi² - nx². The interesting thing about this is that we are already given in deviation form the value of summation xi² as 116. The value of n is given to us seven times and x times n is given to us so the whole square of x times will be 81. So when we plug in these values we get the value of capital xi² which is going to be 683.
Now we have to plug in the simple formula.
So we know the value of capital xi².
We had taken out σ².
The value of n is seven. And small xi² is given to us.
So when we go ahead and when we put these values in this. When we plug this into this fula, we go ahead and get the answer. And the standard error or standard deviation of beta1 comes out to be 0.2282, okay.
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