What is the least-squares regression line with the point (9,13) included in the data set? Data Set o (Type integers or decimals rounded to four decimal places as needed.) y 4 5 80 81 10 11 11 12 13 13 14 10 12 10 This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![**Title: Understanding Least-Squares Regression Line Calculation**
**Objective:**
Determine the least-squares regression line by including the point (9,13) within the given dataset.
**Data Table:**
| x | y |
|----|----|
| 3 | 6 |
| 4 | 5 |
| 5 | 7 |
| 7 | 6 |
| 8 | 9 |
| 8 | 8 |
| 10 | 9 |
| 11 | 9 |
| 11 | 9 |
| 12 | 10 |
| 13 | 12 |
| 13 | 10 |
| 14 | 11 |
**Question presented on the page:**
What is the least-squares regression line with the point (9,13) included in the data set?
\[ \hat{y} = \square x + \square \]
(Type integers or decimals rounded to four decimal places as needed.)
**Instructions:**
- This is a reading assessment question. Ensure the accuracy of your response as only one attempt is allowed.
---
**Explanation of Calculation Steps:**
1. **Collect and Plot Data Points:** Begin by plotting the provided x and y values on a graph, including the point (9,13).
2. **Calculate the Mean of x and y:** Compute the average of the x-values and y-values separately.
3. **Determine the Slope (b):** Use the formula to find the slope:
\[
b = \frac{\sum{(x_i - \overline{x})(y_i - \overline{y})}}{\sum{(x_i - \overline{x})^2}}
\]
4. **Calculate the y-Intercept (a):** Use the formula for the intercept:
\[
a = \overline{y} - b \cdot \overline{x}
\]
5. **Form the Regression Equation:** Integrate the slope and intercept into the linear equation format:
\[
\hat{y} = bx + a
\]
Remember to insert the correct integers or decimals (rounded to four decimal places) into the provided equation format on the website.
**Note:** While this overview serves as a guide, practical application of formulas and input of accurate data remains crucial in solving the regression](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5685ce4-d9f8-4c8e-aa78-bd82f1a4dfdc%2Fc9beaab5-a966-4ac2-95a4-33729567be3a%2F4k8jilr_processed.jpeg&w=3840&q=75)
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