A research was conducted by a company to analyze the influence of year experience to annual sales. There were 10 sales manager collected, and the following data x = year of experience y = annual sales Salesperson Years of Experience Annual Sales ($1,000s) 1 1 80 2 3 100 3 4 110 4 4 115 5 6 106 6 8 118 7 10 123 8 10 120 9 11 119 10 13 140 a. Determine the regression equation! Use the estimated regression equation to predict the annual sales if the year experience is 14 and 15 years! b. Determine the coefficients of correlation and coefficient determination! c. Does the t test indicate a significant relationship between year of experience and annual sales? What is your conclusion? Use the α = 5% d. Test for a significant relationship using F test. What is your conclusion? Use the α = 5%
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 research was conducted by a company to analyze the influence of year experience to annual sales. There were 10 sales manager collected, and the following data x = year of experience y = annual sales
| Salesperson | Years of Experience |
Annual Sales ($1,000s) |
|---|---|---|
| 1 | 1 | 80 |
| 2 | 3 | 100 |
| 3 | 4 | 110 |
| 4 | 4 | 115 |
| 5 | 6 | 106 |
| 6 | 8 | 118 |
| 7 | 10 | 123 |
| 8 | 10 | 120 |
| 9 | 11 | 119 |
| 10 | 13 | 140 |
a. Determine the regression equation! Use the estimated regression equation to predict the annual sales if the year experience is 14 and 15 years!
b. Determine the
c. Does the t test indicate a significant relationship between year of experience and annual sales? What is your conclusion? Use the α = 5%
d. Test for a significant relationship using F test. What is your conclusion? Use the α = 5%
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