
Use the least squares regression line of this data set to predict a value.
Ted works with a property developer building houses close to the coastline in Italy. His boss thinks that demand for the houses will be based primarily on their size. Ted wants to show his boss that proximity to the ocean is also a big factor to consider.
So, he looks at several houses of the same size in the area. He records the distance of each house from the ocean (in kilometers), x. He also notes the number of people who offered to buy each house, y, when it was last put up for sale.
Kilometers from ocean	Offers
1	13
3	11
5	13
7	14
9	14
18	4
The least squares regression line of this data set is:
y=–
0.484x+14.968
How many offers does this line predict for a house 4 kilometers away from the ocean?
Round your answer to the nearest integer.
 _________________offers

We are given the least squares regression line:

\[
y = -0.484x + 14.968
\]

where:
- \(x\) represents the distance of the house from the ocean in kilometers, and
- \(y\) represents the number of offers received for the house.

We need to predict the number of offers for a house that is 4 kilometers away from the ocean (\(x = 4\)).

### Step 1: Substitute \(x = 4\) into the regression equation:

\[
y = -0.484(4) + 14.968
\]

### Step 2: Simplify the equation:

\[
y = -0.484 \times 4 + 14.968
\]
\[
y = -1.936 + 14.968
\]
\[
y = 13.032
\]

### Step 3: Round the result to the nearest integer:

\[
y \approx 13
\]

Thus, the least squares regression line predicts **13 offers** for a house 4 kilometers away from the ocean.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How does proximity to the ocean impact the number of offers based on the slope of the regression line?
2. What is the significance of the intercept \(14.968\) in this context?
3. How would the predicted number of offers change if a house is 10 kilometers away from the ocean?
4. How can you calculate the residual for a house 4 kilometers away from the ocean if you know the actual number of offers?
5. What is the correlation coefficient for this data set, and what does it indicate about the relationship between distance and offers?

**Tip**: The slope of the regression line indicates the change in offers for each additional kilometer a house is from the ocean.

Use the least squares regression line of this data set to predict a value. Ted works with a property developer building houses close to the coastline in Italy. His boss thinks that demand for the houses will be based primarily on their size. Ted wants to show his boss that proximity to the ocean is also a big factor to consider. So, he looks at several houses of the same size in the area. He records the distance of each house from the ocean (in kilometers), x. He also notes the number of people who offered to buy each house, y, when it was last put up for sale. Kilometers from ocean: 1, 3, 5, 7, 9, 18. Offers: 13, 11, 13, 14, 14, 4. The least squares regression line of this data set is: y = -0.484x + 14.968. How many offers does this line predict for a house 4 kilometers away from the ocean? Round your answer to the nearest integer.

Learn how to predict the number of offers for a house based on its proximity to the ocean using the least squares regression line: y = -0.484x + 14.968. In this problem, we calculate the predicted number of offers for a house located 4 kilometers from the ocean. Explore key algebraic concepts and the least squares method in a real estate context. Suitable for Grades 9-12.

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