
South Dakota
8.1 
25.1
Nevada
11.8
30.4
NewJersey
11.8
36.1
Texas
10.0
26.5
Kentucky
8.2
23.2
Maine8.4
25.0
Arizona
9.6
25.3
Wisconsin
10.2
27.4
Maryland
11.2
32.2
Michigan
10.4
27.8
Hawaii
11.5
27.8
Oregon
10.2
27.1
Minnesota
10.3
30.6
Utah
8.5
23.4

The least-squares regression line for these data has a slope of approximately
2.29
.

Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.)
(a)What is the value of the y-intercept of the least-squares regression line for these data? Round your answer to at least two decimal places.

(b)What is the value of the sample correlation coefficient for these data? Round your answer to at least three decimal places.

To solve these questions, we need to calculate the y-intercept of the least-squares regression line and the correlation coefficient using the given data. The slope \( m = 2.29 \) has already been provided.

Let me break down the steps:

### (a) Finding the y-intercept \( b \):
The equation of a regression line is:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept. To calculate the y-intercept \( b \), we use the formula:
\[
b = \bar{y} - m\bar{x}
\]
Where:
- \( \bar{x} \) is the mean of the \( x \)-values (first set of numbers).
- \( \bar{y} \) is the mean of the \( y \)-values (second set of numbers).
- \( m \) is the slope (which is given as 2.29).

We will now calculate the mean values of the \( x \) and \( y \) data, and use them to find \( b \).

### Data:

- **x-values**: 8.1, 11.8, 11.8, 10.0, 8.2, 8.4, 9.6, 10.2, 11.2, 10.4, 11.5, 10.2, 10.3, 8.5
- **y-values**: 25.1, 30.4, 36.1, 26.5, 23.2, 25.0, 25.3, 27.4, 32.2, 27.8, 27.8, 27.1, 30.6, 23.4

Let me compute the mean \( \bar{x} \) and \( \bar{y} \), and then find the y-intercept \( b \).It seems like I can’t do more advanced data analysis right now. Please try again later.

Feel free to try again or ask for clarifications on this problem! If you need help with another mathematical problem, let me know.

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Here are some related questions you might be interested in:

1. How can I calculate the slope of a regression line manually?
2. What is the meaning of the correlation coefficient in regression analysis?
3. How is the standard error of the estimate calculated for a least-squares regression line?
4. What are the assumptions behind least-squares regression?
5. How do outliers affect the least-squares regression line?

**Tip**: Always carry your calculations to a few more decimal places than you plan to round to, as this helps avoid rounding errors in intermediate steps.

The query submitted by the user: South Dakota 8.1 25.1 Nevada 11.8 30.4 NewJersey 11.8 36.1 Texas 10.0 26.5 Kentucky 8.2 23.2 Maine 8.4 25.0 Arizona 9.6 25.3 Wisconsin 10.2 27.4 Maryland 11.2 32.2 Michigan 10.4 27.8 Hawaii 11.5 27.8 Oregon 10.2 27.1 Minnesota 10.3 30.6 Utah 8.5 23.4 The least-squares regression line for these data has a slope of approximately 2.29. (a) What is the value of the y-intercept of the least-squares regression line for these data? (b) What is the value of the sample correlation coefficient for these data?

Learn how to find the y-intercept and sample correlation coefficient for a least-squares regression line, using data from multiple states and a slope of 2.29. Step-by-step guide to solving the problem, including key concepts from linear regression and statistics.

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