A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below. Vacation Days 12 10 2 11 11 13 12 6 10 Sick Days 0 0 8 0 0 0 0 1 0 Find the correlation coefficient: r= Round to 2 decimal places. The equation of the linear regression line is: ˆy = + x (Please show your answers to two decimal places) Use the model to predict the number of sick days taken for an employee who took 7 vacation days this year.
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.
A study was done to look at the relationship between number of vacation days employees take each year and the number of sick days they take each year. The results of the survey are shown below.
| Vacation Days | 12 | 10 | 2 | 11 | 11 | 13 | 12 | 6 | 10 |
|---|---|---|---|---|---|---|---|---|---|
| Sick Days | 0 | 0 | 8 | 0 | 0 | 0 | 0 | 1 | 0 |
- Find the
correlation coefficient : r= Round to 2 decimal places. - The equation of the linear regression line is:
ˆy = + x (Please show your answers to two decimal places) - Use the model to predict the number of sick days taken for an employee who took 7 vacation days this year.
Sick Days = (Please round your answer to the nearest whole number.)
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