Model Summary S R-sq R-sq(adj) 3.75497 84.14% 82.70% Analysis of Variance Source DF SS MS F P Regression 1 822.915 822.915 58.36 0.000 Error 11 155.098 14.100 Total 12 978.012 What is the Correlation Coefficient? And what does the Correlation Coefficient tell you about the direction and strength of the relationship between these variables? Using the P value or the critical values for the Pearson coefficient Critical Values Table for Pearson Coefficient is there enough evidence to support a relationship at the 5% level of significance (α = .05) for these variables? Explain how you arrived at your answer. d. Using the result for the Correlation Coefficient compute the Coefficient of Determination (r-squared). Interpret this value…what information does this give us concerning Age and Annual Salaries?
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.
Model Summary
| S | R-sq | R-sq(adj) |
| 3.75497 | 84.14% | 82.70% |
Analysis of Variance
| Source | DF | SS | MS | F | P |
| Regression | 1 | 822.915 | 822.915 | 58.36 | 0.000 |
| Error | 11 | 155.098 | 14.100 | ||
| Total | 12 | 978.012 |
- What is the
Correlation Coefficient? And what does the Correlation Coefficient tell you about the direction and strength of the relationship between these variables? - Using the P value or the critical values for the Pearson coefficient Critical Values Table for Pearson Coefficient is there enough evidence to support a relationship at the 5% level of significance (α = .05) for these variables? Explain how you arrived at your answer.
- d. Using the result for the Correlation Coefficient compute the Coefficient of Determination (r-squared). Interpret this value…what information does this give us concerning Age and Annual Salaries?
The coefficient of correlation between any two variables, is a measure of association between the variables. Its value lies between -1 and 1 (including 1 and -1).
If the two variables are strongly correlated, then the value of coefficient of correlation is close to ±1 and if the two variables are not at all correlated, then the value of coefficient of correlation is close to 0.
The coefficient of determination represents the percentage of variability in the sampled values of dependent variable that can be explained on the basis of independent variable.
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