A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data. Years of employed (x) 2 3 10 7 8 15 3 1 11 Sales (y) 31 33 78 62 65 70 48 55 64 (c) Find the equation of least square regression. (d) What would be the predicted sales if the sales representative was employed by the firm for 20 years. (e) Find the residual when the sales representative was employed by the firm for 15 years.
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 manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the equation of the regression line for the given data.
| Years of employed (x) | 2 | 3 | 10 | 7 | 8 | 15 | 3 | 1 | 11 |
| Sales (y) | 31 | 33 | 78 | 62 | 65 | 70 | 48 | 55 | 64 |
(c) Find the equation of least square regression.
(d) What would be the predicted sales if the sales representative was employed by the firm for 20 years.
(e) Find the residual when the sales representative was employed by the firm for 15 years.
Given Information :
A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month.
The independent variable is , and the dependent variable is . In order to compute the regression coefficients, the following table needs to be used:
| Years of employed X | Sales Y | X*Y | X2 | Y2 | |
| 2 | 31 | 62 | 4 | 961 | |
| 3 | 33 | 99 | 9 | 1089 | |
| 10 | 78 | 780 | 100 | 6084 | |
| 7 | 62 | 434 | 49 | 3844 | |
| 8 | 65 | 520 | 64 | 4225 | |
| 15 | 70 | 1050 | 225 | 4900 | |
| 3 | 48 | 144 | 9 | 2304 | |
| 1 | 55 | 55 | 1 | 3025 | |
| 11 | 64 | 704 | 121 | 4096 | |
| Sum = | 60 | 506 | 3848 | 582 | 30528 |
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