Answer :
Answer:
[tex]\text{Selling price} = \$1000e^{5.6}[/tex]
The selling price of house is approximately 270.4264 thousand dollars.
Step-by-step explanation:
We are given the following in the question:
A linear model gives the relation between natural logarithm of price, in thousands of dollars, and size, in 100 square feet.
[tex]\ln( \text{price})=2.08+0.11(\text{size})[/tex]
Let p be the price and s be the size.
[tex]\ln(p) = 2.08 + 0.11(s)[/tex]
We have to approximate the selling price for a house with a size of 3,200 square feet.
Thus, we put s = 32
[tex]\ln(p) = 2.08 + 0.11(32)\\\ln(p) = 5.6\\p = e^{5.6}\\p = 270.4264\\\text{Selling price} = \$1000e^{5.6}[/tex]
Thus, the selling price of house is approximately 270.4264 thousand dollars.
Final answer:
The regression equation provided in the question can be solved by substitifying the size value (in 100 sq ft units) into the equation and subsequently calculating the exponent of the resulting value to obtain the predicted house price.
Explanation:
The real estate agent has given a model which is ln(price) = 2.08 + 0.11*(size). To predict the selling price of a house that measures 3,200 square feet, we first convert the size in terms of 100 square feet units, which is 32 units (3200/100).
Substituting this into the regression equation, we get ln(price) = 2.08 + 0.11*32. Now to get the price, we need to calculate the exponent of the resultant value because it was initially taken as natural logarithm.
The resultant value of the expression gives us the predicted selling price of the house. In the real-world scenario, factors like location, construction quality, etc., also play crucial roles.
Learn more about Mathematics: Regression Analysis here:
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