±0.811 We can conclude that Suppose the coefficient of correlation for two variable is r=-0.901 and the critical values are O There is a statistically significant correlation O The correlation is not statistically significant
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.
![### Correlation Coefficient Analysis
#### Problem Statement:
Suppose the coefficient of correlation for two variables is \( r = 0.901 \) and the critical values are \( \pm 0.811 \). We can conclude that ________.
#### Multiple Choice Options:
- \( \bigcirc \) There is a statistically significant correlation
- \( \bigcirc \) The correlation is not statistically significant
### Explanation:
The coefficient of correlation, represented as \( r \), measures the strength and direction of a linear relationship between two variables. The critical value helps in determining if this correlation is statistically significant or not. Here, \( r = 0.901 \) is compared against the critical values \( \pm 0.811 \).
- If \( r \) falls outside the range of these critical values (i.e., \( r > 0.811 \) or \( r < -0.811 \)), the correlation is considered statistically significant.
- If \( r \) falls within this range (i.e., \( -0.811 \leq r \leq 0.811 \)), the correlation is not statistically significant.
In this case, since \( r = 0.901 \) is greater than \( 0.811 \), we can conclude that:
\[ \bigcirc \ \text{There is a statistically significant correlation} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfef55d1-e74e-4acc-a65e-b6e34bf1c85d%2F7aadc215-6611-4e1d-a1b6-c89d5a5aa735%2Fzop1vj_processed.jpeg&w=3840&q=75)
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