It is believed that standardized test scores, such as SAT, is a good predictor of first-year college students' GPA. X y -1200 1120 3.2 2.5 1000 2.7 1420 1280 750 1100 3.5 2.9 2.2 2.3 1. Find the the correlation coefficient. Round your final answer to four decimal places. T= 2. Write the regression equation below. Round all numbers to four decimal places. 3. Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places. 4. What percentage of variation in GPAS can be explained by students' SAT scores? Round your final answer to two decimal places. %
It is believed that standardized test scores, such as SAT, is a good predictor of first-year college students' GPA. X y -1200 1120 3.2 2.5 1000 2.7 1420 1280 750 1100 3.5 2.9 2.2 2.3 1. Find the the correlation coefficient. Round your final answer to four decimal places. T= 2. Write the regression equation below. Round all numbers to four decimal places. 3. Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places. 4. What percentage of variation in GPAS can be explained by students' SAT scores? Round your final answer to two decimal places. %
MATLAB: An Introduction with Applications
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![**Predicting First-Year College GPA from SAT Scores**
It is believed that standardized test scores, such as SAT, are good predictors of first-year college students' GPA.
Below is a table displaying SAT scores (x) and corresponding first-year GPA (y):
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1200 & 1120 & 1000 & 1420 & 1280 & 750 & 1100 \\
\hline
y & 3.2 & 2.5 & 2.7 & 3.5 & 2.9 & 2.2 & 2.3 \\
\hline
\end{array}
\]
1. **Find the correlation coefficient. Round your final answer to four decimal places.**
\[
r = \_\_\_\_
\]
2. **Write the regression equation below. Round all numbers to four decimal places.**
\[
\hat{y} = \_\_\_\_
\]
3. **Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places.**
\[
\_\_\_\_
\]
4. **What percentage of variation in GPAs can be explained by students' SAT scores? Round your final answer to two decimal places.**
\[
\_\_\_\_ \%
\]
---
In this exercise, you will calculate the correlation coefficient, derive the regression equation, make predictions based on the regression model, and interpret the percentage of variation explained by the model. These steps are crucial in understanding the relationship between SAT scores and first-year college GPAs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F402afc63-9cac-4d1f-a06a-b4853df74aca%2F18af1baf-570c-4715-b867-0f3335fbdfd5%2F53axrpb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Predicting First-Year College GPA from SAT Scores**
It is believed that standardized test scores, such as SAT, are good predictors of first-year college students' GPA.
Below is a table displaying SAT scores (x) and corresponding first-year GPA (y):
\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
x & 1200 & 1120 & 1000 & 1420 & 1280 & 750 & 1100 \\
\hline
y & 3.2 & 2.5 & 2.7 & 3.5 & 2.9 & 2.2 & 2.3 \\
\hline
\end{array}
\]
1. **Find the correlation coefficient. Round your final answer to four decimal places.**
\[
r = \_\_\_\_
\]
2. **Write the regression equation below. Round all numbers to four decimal places.**
\[
\hat{y} = \_\_\_\_
\]
3. **Using the data shown above, predict a student's first-year GPA when the student scores a 1275 on the SAT. Round your final answer to two decimal places.**
\[
\_\_\_\_
\]
4. **What percentage of variation in GPAs can be explained by students' SAT scores? Round your final answer to two decimal places.**
\[
\_\_\_\_ \%
\]
---
In this exercise, you will calculate the correlation coefficient, derive the regression equation, make predictions based on the regression model, and interpret the percentage of variation explained by the model. These steps are crucial in understanding the relationship between SAT scores and first-year college GPAs.
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