Question

A real estate agent wants to predict the selling price of single-family homes from the size of each house. A scatterplot created from a sample of houses shows an exponential relationship between price, in thousands of dollars, and size, in 100 square feet. To create a linear model, the natural logarithm of price was taken and the least-squares regression line was given as ln( price ˆ )=2.08+0.11(size) ln⁡(price^)=2.08+0.11(size) . Based on the model, which of the following is closest to the predicted selling price for a house with a size of 3,200 square feet?

Answer 1

Answer:

$\text{Selling price} = \ 1000e^{5.6}$

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.

$\ln( \text{price})=2.08+0.11(\text{size})$

Let p be the price and s be the size.

$\ln(p) = 2.08 + 0.11(s)$

We have to approximate the selling price for a house with a size of 3,200 square feet.

Thus, we put s = 32

$\ln(p) = 2.08 + 0.11(32)\\\ln(p) = 5.6\\p = e^{5.6}\\p = 270.4264\\\text{Selling price} = \ 1000e^{5.6}$

Thus, the selling price of house is approximately 270.4264 thousand dollars.