Linear Regression and Correlation. y 1 1.8 2.3 5.9 -7.5 5 -7.3 6 -3.2 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 HẠ: slope = 0 for the alternative hypothesis.) Use at least 3 decimal places. (Round if necessary) P-value = At the alpha = 0.01 significance level, is the correlation significant? O No Yes, significant correlation co mo nmN 2. 3. 4.
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
### Table of Values
\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 1.8 \\
2 & 2.3 \\
3 & 5.9 \\
4 & -7.5 \\
5 & -7.3 \\
6 & -3.2 \\
\hline
\end{array}
\]
### Linear Regression Equation
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)**
\[
y = \_\_\_\_\_ x + \_\_\_\_\_
\]
### Correlation Coefficient
Compute the correlation coefficient for this data set. Use at least 3 decimal places. (Round if necessary)
\[
r = \_\_\_\_\_
\]
### P-value Calculation
Compute the P-value (Use \( H_A: \text{slope} \neq 0 \) for the alternative hypothesis.)
**Use at least 3 decimal places. (Round if necessary)**
\[
P\text{-value} = \_\_\_\_\_
\]
### Significance Test
At the \(\alpha = 0.01\) significance level, is the correlation significant?
- \( \circ \) No
- \( \circ \) Yes, significant correlation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa218d9b0-33cd-49fb-8966-615774819802%2F466c3891-fcbb-4eb0-99ae-68e987e3591c%2F8jshxaf_processed.png&w=3840&q=75)
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