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In Table 5 normalized house price is provided. A machine learning algorithm is trained on the House size for predicting the House price. The predicted price can be expressed by the equation $Yp=a+bX$. The sum of squared error $(SSE)$ can be expressed with the formula

$SSE=\frac{1}{2} (actual \ house \ price- predicted\ house \ price)^{2} = \frac{1}{2}(Y-Yp)^{2}$

Calculate the error gradient $\frac{d}{db} SSE$

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Wouldnt this just result in $2(Y - Yp)/2$

$\frac{d}{db} SSE = Y - (a + bx)$ ?

We get the value $a = 0.45$ from the table which makes $b = 0.77$

Feels like I am missing something I dont know if I am doing the calculation the way the question wants me.

zellez11
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  • I don't understand the predictor...it's terrible. Specifically it is heavily biased, every prediction is much too high. You could dramatically improve the predictor just by subtracting $.30$ or something from every value. What exactly is it meant to be optimizing? – lulu May 01 '23 at 13:43
  • I am supposed to learn how to calculate the error gradient based on the formulas given and nothing much maybe in a future question it will ask me about this not there get. I am just questioning if I have solved what they are asking in the right way – zellez11 May 01 '23 at 13:46
  • Nor do I understand your "sum of squared errors". There's no sum here, and why do you have a factor of $\frac 12$? – lulu May 01 '23 at 13:48
  • I dont know either it is just written like that – zellez11 May 01 '23 at 13:49
  • So, assuming you meant to write $SSE=\sum (Y_i-a-bX_i)^2$ you can just differentiate term by term. to get $-2\sum X_i(Y_i-a-bX_i)$. Maybe the $\frac 12$ is intended to kill off that factor of $2$, but that's not usually done in writing out the error function. – lulu May 01 '23 at 13:51

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