A real estate agent wants to predict the selling price of single-family homes from the size of each house. A scatterplot created

Question

Nadusha1986

2 months ago

15

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?

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-03-25T08:23:20+03:00

Answer:

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

The estimated selling price of the house is around 270.4264 thousand dollars.

Step-by-step reasoning:

The problem provides the following information:A linear equation relates the natural logarithm of the price (in thousands of dollars) to the size (in hundreds of square feet).

$\ln( \text{price})=2.08+0.11(\text{size})$ Let p denote the price and s represent the size.

$\ln(p) = 2.08 + 0.11(s)$ We are tasked with estimating the selling price of a 3,200 square foot house.

Thus, s equals 32.

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

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