We appreciate your visit to Linear Regression Suppose the following are prices of recently sold houses in some neighborhood House area in square feet 1235 1691 1824 2000 Sold at. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
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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