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[Stats] OLS with a given intercept

Hi, hope someone can help me with this question as I don't think I really understand.

We want to find the OLS estimate of b given that yi=2+bxi+uiy_i = 2 + bx_i + u_i. That is, given that the intercept is 2.

So I know that when we're estimating b using OLS we use:

b^=∑i=1n(xi−xˉ)(yi−yˉ)∑i=1n(xi−x^)2\hat{b} = \frac{\sum_{i=1}^n (x_i-\bar{x})(y_i-\bar{y})}{\sum_{i=1}^n (x_i-\hat{x})^2}

We've also looked at the case where we state that the line must go through the origin, and there:

b^=∑i=1nxiyi∑i=1nxi2\hat{b} = \frac{\sum_{i=1}^n x_iy_i}{\sum_{i=1}^n x_i^2}

So is the question just asking me to consider that instead of going through the origin, we pass through (0,2)? Do I just use yi−2y_i - 2 instead of yiy_i to estimate b? Really confusing myself.
Hi there,

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