11. The data pairs (x, y) give U.S. average annual public college tuition y (in dollars) x years after 1997. (0, 2271), (1, 2360), (2, 2430), (3, 2506), (4, 2562), (5, 2727), (6, 2928) a) Find the best-fitting line for the data by plugging the info into the table on your calculator and doing a STATPLOT. b) Write the value of r. What is the meaning of your r value?
11. The data pairs (x, y) give U.S. average annual public college tuition y (in dollars) x years after 1997. (0, 2271), (1, 2360), (2, 2430), (3, 2506), (4, 2562), (5, 2727), (6, 2928) a) Find the best-fitting line for the data by plugging the info into the table on your calculator and doing a STATPLOT. b) Write the value of r. What is the meaning of your r value?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Understanding Linear Regression and Correlation with U.S. College Tuition Data
**Problem 11:**
The data pairs \((x, y)\) provide information on the U.S. average annual public college tuition \(y\) (in dollars) \(x\) years after 1997. The data are as follows:
\[
\begin{align*}
(0, 2271), \\
(1, 2360), \\
(2, 2430), \\
(3, 2506), \\
(4, 2562), \\
(5, 2727), \\
(6, 2928)
\end{align*}
\]
**a)** Using a statistical calculator or software, input the data to create a table and perform a STATPLOT to determine the best-fitting line for these data points.
**b)** Calculate the correlation coefficient \(r\) and interpret its meaning in this context.
---
**Instructions to Students:**
1. **Data Entry and Plotting:**
- Enter the given pairs of \((x, y)\) data into your graphing calculator or statistical software.
- Use the STATPLOT feature to visualize the data points on a scatter plot.
- Apply linear regression to find the line of best fit, which will provide the equation of a line that best approximates the data points.
2. **Finding the Correlation Coefficient:**
- After plotting the data and finding the best-fitting line, your calculator/software will typically provide the correlation coefficient \(r\).
- The value of \(r\) ranges from \(-1\) to \(1\). In this scenario, \(r\) indicates how well the linear model fits the data.
3. **Interpreting \(r\):**
- If \(r\) is close to \(1\), it implies a strong positive linear relationship between the number of years after 1997 and the average annual public college tuition.
- If \(r\) is close to \(-1\), it indicates a strong negative linear relationship.
- If \(r\) is close to \(0\), it suggests that there is little to no linear relationship between the variables.
By analyzing these data points, you will be able to understand the trend in public college tuition over the years and interpret how well a linear model explains this trend.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F479561bb-cade-44a0-8f0b-055029c2f8fc%2F763dc1a1-81a0-4213-b7a5-a519837ca87a%2Fpy771xc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Linear Regression and Correlation with U.S. College Tuition Data
**Problem 11:**
The data pairs \((x, y)\) provide information on the U.S. average annual public college tuition \(y\) (in dollars) \(x\) years after 1997. The data are as follows:
\[
\begin{align*}
(0, 2271), \\
(1, 2360), \\
(2, 2430), \\
(3, 2506), \\
(4, 2562), \\
(5, 2727), \\
(6, 2928)
\end{align*}
\]
**a)** Using a statistical calculator or software, input the data to create a table and perform a STATPLOT to determine the best-fitting line for these data points.
**b)** Calculate the correlation coefficient \(r\) and interpret its meaning in this context.
---
**Instructions to Students:**
1. **Data Entry and Plotting:**
- Enter the given pairs of \((x, y)\) data into your graphing calculator or statistical software.
- Use the STATPLOT feature to visualize the data points on a scatter plot.
- Apply linear regression to find the line of best fit, which will provide the equation of a line that best approximates the data points.
2. **Finding the Correlation Coefficient:**
- After plotting the data and finding the best-fitting line, your calculator/software will typically provide the correlation coefficient \(r\).
- The value of \(r\) ranges from \(-1\) to \(1\). In this scenario, \(r\) indicates how well the linear model fits the data.
3. **Interpreting \(r\):**
- If \(r\) is close to \(1\), it implies a strong positive linear relationship between the number of years after 1997 and the average annual public college tuition.
- If \(r\) is close to \(-1\), it indicates a strong negative linear relationship.
- If \(r\) is close to \(0\), it suggests that there is little to no linear relationship between the variables.
By analyzing these data points, you will be able to understand the trend in public college tuition over the years and interpret how well a linear model explains this trend.
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