Answer :
The predicted price of the new house on the market with an area of 1900 square feet is $697,620.The Linear Regression model is a supervised learning algorithm that predicts the target variable as a continuous value.
In the problem above, the Linear Regression algorithm is used to predict the prices of a house based on its square footage.
The regression equation,
y = wx + b, represents the equation of a straight line,
where w represents the slope of the line, and b represents the y-intercept. The two weights are w1 and w0.
In order to calculate the two weights, we need to follow the below steps:
First, we need to find the mean of both x (house area in square feet) and y (sold price).
x = [1235, 1691, 1824, 2000]
y = [630, 780, 825, 999]
mean_x = (1235 + 1691 + 1824 + 2000)/4
= 1687.5
mean_y = (630 + 780 + 825 + 999)/4
= 808.5
Next, we need to calculate the covariance of x and y.covariance
= ∑(xi - mean_x)(yi - mean_y) / (n - 1)
where n is the number of observations.covariance
= ((1235 - 1687.5)(630 - 808.5) + (1691 - 1687.5)(780 - 808.5) + (1824 - 1687.5)(825 - 808.5) + (2000 - 1687.5)(999 - 808.5)) / (4 - 1)
covariance = 72245.8333
Next, we need to calculate the variance of x.
variance =[tex]sum_{n - 1}^{xi - mean_x\^2[/tex]
variance =[tex]((1235 - 1687.5)^2 + (1691 - 1687.5)^2 + (1824 - 1687.5)^2 + (2000 - 1687.5)^2) / (4 - 1)[/tex]
variance = 175722.9167
Now we can calculate w1 and w0.w1
= covariance / variancew1
= 72245.8333 / 175722.9167w1
= 0.4119w0
= mean_y - w1 * mean_xw0
= 808.5 - 0.4119 * 1687.5w0
= -142.58
So the equation of the line is:y = 0.4119x - 142.58
Finally, to predict the price of a new house on the market with an area of 1900 sf,
we substitute x = 1900 in the equation and solve for y:
y = 0.4119 * 1900 - 142.58y
= 697.62
Therefore, the predicted price of the new house on the market with an area of 1900 square feet is $697,620.
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