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We want to predict the selling price of a house in Newburg Park, Florida, based on the distance the house lies from the beach. Suppose that we're given the data in the table below. These data detail the distance from the beach (x, in miles) and the selling price (y, in thousands of dollars) for each of a sample of sixteen homes sold in Newburg Park in the past year. The data are plotted in the scatter plot in Figure 1. Also given is the product of the distance from the beach and the house price for each of the sixteen houses. (These products, written in the column labelled "xy", may aid in calculations.) What is the sample correlation coefficient for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.

To calculate the sample correlation coefficient \( r \) for the given data, we'll use the formula:

\[
r = \frac{n\sum{xy} - \sum{x}\sum{y}}{\sqrt{\left[n\sum{x^2} - (\sum{x})^2\right]\left[n\sum{y^2} - (\sum{y})^2\right]}}
\]

Where:
- \( n \) is the number of data points.
- \( \sum{xy} \) is the sum of the product of \( x \) and \( y \) for each pair.
- \( \sum{x} \) is the sum of all \( x \) values.
- \( \sum{y} \) is the sum of all \( y \) values.
- \( \sum{x^2} \) is the sum of the squares of \( x \) values.
- \( \sum{y^2} \) is the sum of the squares of \( y \) values.

Let's extract the values from the table in the image and perform the calculations.

1. **Extract the values from the table**: 
   - \( x \) (Distance from the beach, in miles)
   - \( y \) (Selling price, in thousands of dollars)
   - \( xy \) (Product of distance and selling price)

2. **Compute the necessary sums**:
   - \( \sum{x} \)
   - \( \sum{y} \)
   - \( \sum{xy} \)
   - \( \sum{x^2} \)
   - \( \sum{y^2} \)

3. **Plug the values into the correlation coefficient formula** and compute \( r \).

I'll start by extracting the data from the image and computing the sums needed for the calculation.The sample correlation coefficient \( r \) for the given data is approximately **0.136** (rounded to three decimal places).

This suggests a very weak positive linear relationship between the distance from the beach and the selling price of the homes in Newburg Park.

Would you like further details or have any other questions?

### Related Questions:
1. What does the correlation coefficient signify in this context?
2. How would you interpret a correlation coefficient close to 0?
3. What is the impact of outliers on the correlation coefficient?
4. Can the correlation coefficient be used to make predictions?
5. How would you calculate the coefficient of determination \( r^2 \) from \( r \)?
6. How would the correlation change if one outlier was removed from the data?
7. What are other methods to analyze the relationship between two variables?
8. How can the accuracy of the correlation coefficient be tested?

**Tip:** The correlation coefficient \( r \) only measures the strength and direction of a linear relationship; it doesn't imply causation.

Learn how to calculate the sample correlation coefficient using data on house prices and distances from the beach in Newburg Park, Florida. Understand the statistical method used to measure the strength and direction of the linear relationship between variables.

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