<p>If <span class="math-container">$X$</span> is constant it is impossible to find the regression equation because regression coefficients <span class="math-container">$\beta_i$</span> are given by:</p>
<p><span class="math-container">$$\beta_i = \frac{cov(Y, X_i)}{var(X_i)}$$</span></p>
<p>if you fix <span class="math-container">$X$</span> to be always 5 the variance of <span class="math-container">$X$</span> is 0 and division by 0 is undefined.</p>

CC BY-SA 4.0
2024-04-24T13:12:55.807Z
2024-04-24T13:12:55.807Z
1muflon1
<p>If there is no constant in the regression, then
<span class="math-container">$$ \widehat{\beta} = \frac{\sum_i x_iy_i}{\sum_i x_i^2} = 5\frac{\sum_i y_i}{5^2N} = \frac{\bar{y}}{5}.$$</span>
It is not a slope, however, as <span class="math-container">$x_i$</span> is constant.</p>

CC BY-SA 4.0
2024-04-25T08:28:58.270Z
2024-04-25T08:52:16.093Z
2024-04-25T08:52:16.093Z
Bertrand
<p>I wanted to know how this equation will look like and how we will be able to calculate the slope coefficient.</p>

<econometrics><regression>
In a regression of Yon X, the value of X is fixed at 5. Find the regression equation
Sakshi Dubey
# In a regression of Yon X, the value of X is fixed at 5. Find the regression equation

(Asked by: username_0 on 2024-04-24)

I wanted to know how this equation will look like and how we will be able to calculate the slope coefficient.

**Tags:** econometrics, regression


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## 2 answers

### Answer by username_1 on 2024-04-24. Score: 2

If $X$ is constant it is impossible to find the regression equation because regression coefficients $\beta\_i$ are given by:

$$\beta\_i = \frac{cov(Y, X\_i)}{var(X\_i)}$$

if you fix $X$ to be always 5 the variance of $X$ is 0 and division by 0 is undefined.


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### Answer by username_2 on 2024-04-25. Score: 2

If there is no constant in the regression, then
$$ \widehat{\beta} = \frac{\sum\_i x\_iy\_i}{\sum\_i x\_i^2} = 5\frac{\sum\_i y\_i}{5^2N} = \frac{\bar{y}}{5}.$$
It is not a slope, however, as $x\_i$ is constant.


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