For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x. X 6 12 14 6 9 13 15 9 Y 300 408 560 252 288 650 630 522 (a) Determine the least-squares regression line and interpret its slope (b) For an employee who has been with the firm 10 years, what is the predicted number of shares owned? (c) Is there a statistical significance between years of service and ownership of company stocks? (use α=0.05α=0.05)
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.
For a sample of 8 employees, a personnel director has collected the following data on ownership of company stock, y, versus years with the firm, x.
| X | 6 | 12 | 14 | 6 | 9 | 13 | 15 | 9 |
| Y | 300 | 408 | 560 | 252 | 288 | 650 | 630 | 522 |
(a) Determine the least-squares regression line and interpret its slope
(b) For an employee who has been with the firm 10 years, what is the predicted number of shares owned?
(c) Is there a statistical significance between years of service and ownership of company stocks? (use α=0.05α=0.05)
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