The following table contains the dollar raises (raise) given to five employee, the number of days of work they missed in the prior year (missed), and the performance score (score) they received from their manager (where 1 is the lowest and 3 is the highest). State Raise Missed Score Employee 1 5 2 3 Employee 2 2 8 2 Employee 3 4 3 2 Employee 4 3 4 2 Employee 5 1 8 1
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.
The following table contains the dollar raises (raise) given to five employee, the number of days of work they missed in the prior year (missed), and the performance score (score) they received from their manager (where 1 is the lowest and 3 is the highest).
| State | Raise | Missed | Score |
| Employee 1 | 5 | 2 | 3 |
| Employee 2 | 2 | 8 | 2 |
| Employee 3 | 4 | 3 | 2 |
| Employee 4 | 3 | 4 | 2 |
| Employee 5 | 1 | 8 |
1 |
Use the data above to examine the relationship between raises and manager score.a) What assumption is required in order to use regression through the origin when regressing raise on manager score? Do you think this is a reasonable assumption in this case? Explain.b) Compute the regression through the origin coefficient and write the resulting equation.c) Interpret the regression coefficient in a sentence.d) What is the predicted raise for an employee with a score of 3? How does this compare to the actual raise received by Employee 1?
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