y 2 6.32 9.28 4 0.14 5 0.7 6 -4.04 7 3.22 Compute the equation of the linear regression line in the form y = mx + b, where m is the slope and b is the intercept. Use at least 3 decimal places. (Round if necessary) y = x + Compute the correlation coeficient for this data set. Use at least 3 decimal places. (Round if necessary) r= Compute the P-value (Use H4: slope = 0 for the alternative hypothesis.) Use at least 3 decimal places. (Round if necessary) P-value = At the alpha = 0.05 significance level, is the correlation significant? O Yes, significant correlation O No 3.
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.
![### Linear Regression and Correlation
| x | y |
|----|-------|
| 2 | 6.32 |
| 3 | 9.28 |
| 4 | 0.14 |
| 5 | 0.7 |
| 6 | -4.04 |
| 7 | 3.22 |
Compute the equation of the linear regression line in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the intercept.
Use at least 3 decimal places. (Round if necessary)
\[ y = \_\_\_\_\_ x + \_\_\_\_\_ \]
Compute the correlation coefficient for this data set. Use at least 3 decimal places. (Round if necessary)
\[ r = \_\_\_\_\_ \]
Compute the P-value (Use \( H_A \): slope \(\neq 0\) for the alternative hypothesis.)
Use at least 3 decimal places. (Round if necessary)
\[ \text{P-value} = \_\_\_\_\_ \]
At the alpha = 0.05 significance level, is the correlation significant?
- [ ] Yes, significant correlation
- [ ] No
### Description of Graphs or Diagrams
The provided table displays the corresponding values of the variables \( x \) and \( y \), which will be used to perform linear regression analysis and correlation computation.
1. **Equation of the Linear Regression Line**:
- This will derive a linear equation \( y = mx + b \) that best fits the data.
- \( m \) (slope) and \( b \) (intercept) are computed values that will be filled in.
2. **Correlation Coefficient (\( r \))**:
- This indicates the strength and direction of the linear relationship between \( x \) and \( y \).
3. **P-value**:
- This evaluates the statistical significance of the observed correlation.
4. **Significance Check**:
- Based on the computed P-value and the specified \( \alpha \) level of 0.05, determine if the observed correlation is statistically significant.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa218d9b0-33cd-49fb-8966-615774819802%2Fd393a0d7-ad51-4045-856c-1f8f707775b4%2F9kjmr2_processed.png&w=3840&q=75)

Step by step
Solved in 3 steps with 3 images









