We appreciate your visit to Based on the housing data below use linear regression to estimate a fair price for a 1900 ft² home Square Feet House Price in thousands. 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 solution is Option D.
The fair price of a 1900 ft² home is given by the equation A = $ 176,000
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the square feet of the house be represented as x
Let the number of houses be represented as y
Let the first point be P ( 1400 , 105)
Let the second point be Q ( 1500 , 183 )
Now , the slope of the equation is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = ( 183 - 105 ) / 1500 - 1400
Slope m = 78 / 100
Slope m = 0.78
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 1400 = 0.78 ( x - 105 )
On simplifying the equation , we get
y - 1400 = 0.78x - 81.9
Adding 1400 on both sides of the equation , we get
y = 0.78x + 1318.1
Therefore , the value of y is 0.78x + 1318.1
Hence , the equation of line is 0.78x + 1318.1 and the price is $ 176,000
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