<p><span class="math-container">$y_t = B_0 + B_1t$</span> </p>

<p>I have proved <span class="math-container">$B_0 = \bar{y} - B_1t$</span> </p>

<p>I have found <span class="math-container">$B_1 = \frac{\sum_{t=1}^T t \cdot (y_t - \bar{y})} {\sum_{t=1}^T t \cdot (t - \bar{t})} $</span></p>

<p>However I'm supposed to have <span class="math-container">$B_1 = \frac{ \sum_{t=1}^T y_t \cdot (t - \bar{t})} {\sum_{t=1}^T t \cdot (t - \bar{t})} $</span></p>

<p>Was just wondering if anyone could point out where I'm going wrong?</p>

CC BY-SA 4.0
2020-05-05T13:18:48.193Z
Did you want to write $\bar{y}$?  The tex command for this is \bar{y}.
Adam Bailey
CC BY-SA 4.0
2020-05-05T19:30:50.650Z
Is your initial equation: yt=B0−B1t or should it be a "+" sign? Since your desired estimation formula is that of yt = B0 +B1t
Poorvi
CC BY-SA 4.0
2020-05-05T23:47:54.837Z
You are already correct. The second equation for $B_1$ is incorrect.
Walrasian Auctioneer
CC BY-SA 4.0
2020-05-06T04:47:48.360Z
https://www.google.com/search?q=derive+ols+estimator&oq=derive+OLS+estimator&aqs=chrome.0.0l8.2615j0j8&sourceid=chrome&ie=UTF-8#kpvalbx=_3z2yXtq-G5mtytMPuOed2Ag42     would this link help?
Mike J
CC BY-SA 4.0
2020-05-06T13:39:48.253Z
They are equal: $\sum_{t=1}^T (a_t-\bar{a})b_t = \sum_{t=1}^T a_t (b_t-\bar{b}) = \sum_{t=1}^T (a_t-\bar{a})(b_t-\bar{b})$.
chan1142
<econometrics>
How to derive OLS estimator?
Mark
# How to derive OLS estimator?

(Asked by: username_0 on 2020-05-05)

$y\_t = B\_0 + B\_1t$

I have proved $B\_0 = \bar{y} - B\_1t$

I have found $B\_1 = \frac{\sum\_{t=1}^T t \cdot (y\_t - \bar{y})} {\sum\_{t=1}^T t \cdot (t - \bar{t})} $

However I'm supposed to have $B\_1 = \frac{ \sum\_{t=1}^T y\_t \cdot (t - \bar{t})} {\sum\_{t=1}^T t \cdot (t - \bar{t})} $

Was just wondering if anyone could point out where I'm going wrong?

**Tags:** econometrics

> **Comments:**
> **username_1**: Did you want to write $\bar{y}$?  The tex command for this is \bar{y}.  
> **username_2**: Is your initial equation: yt=B0−B1t or should it be a "+" sign? Since your desired estimation formula is that of yt = B0 +B1t  
> **username_3**: You are already correct. The second equation for $B_1$ is incorrect.  
> **username_4**: https://www.google.com/search?q=derive+ols+estimator&oq=derive+OLS+estimator&aqs=chrome.0.0l8.2615j0j8&sourceid=chrome&ie=UTF-8#kpvalbx=_3z2yXtq-G5mtytMPuOed2Ag42     would this link help?  
> **username_5**: They are equal: $\sum_{t=1}^T (a_t-\bar{a})b_t = \sum_{t=1}^T a_t (b_t-\bar{b}) = \sum_{t=1}^T (a_t-\bar{a})(b_t-\bar{b})$.  

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## 0 answers

