(Solved): machien learning - linear regration We consider the following data set concerning House pricing. Th ...

We consider the following data set concerning House pricing. The table presents the values of two features (Area and Number of rooms) and the house price. 1- One variable Linear Regression We consider only the Area feature for estimating the price of house. We suggest to use a Linear Regression model the relationship between the Area $$(x)$$ - House price $$(y)$$. $$(y=wx+b)$$ a) Compute $$w$$ and $$b$$ the parameters of the Linear regression b) Compute the obtained cost function $$J(w,b)=\underset{i=1}{\overset{m}{?}}{\left(y_i?{\hat{y}}_i\right)}^2$$ c) Compute the corresponding $$R^2$$ d) For computing the values of $$w,b$$, we suggest using the Gradient Descent, with a learning rate $$?=0.1$$. Compute the update of the parameters for three iterations of the GD. 2- Multivariable Linear Regression In this case both features re considered to build a Linear Regression. $$y=w_2{x}_2+w_1{x}_1+w_0$$ Where $$x_1$$ and $$x_2$$ correspond respectively to the features Area and number of rooms. a) Scaling of the data according to the two following steps - Subtract the mean value of each feature from the dataset. - After subtracting the mean, additionally scale (divide) the feature values by their respective standard deviations. b) Give the normal equations that compute the linear regression parameter vector $$W={\left(w_0,w_1,w_2\right)}^T$$ (fill the matrix $$X_{?}b$$ and the vector $$Y$$ by the appropriate values).