The table below shows the number of interceptions (balls caught by opponent team during passing) during the season by seven randomly selected National Football League teams and the number of games those teams won during the season. A simple linear regression model, , is developed with “Wins” being the dependent variable and “Interceptions” as the independent variable. Wins Interceptions 3 28 6 19 11 16 14 6 10 9 8 25 8 11 Following the Ordinary Least Squares method, find the OLS line: , based on the regression model above: b0 = 12.105; b1= -2.0435 b0 = 12.7676; b1= -1.6896 b0 = 14.213; b1= -0.346 b0 = 2.063; b1= -0.115 Using the OLS results and find the predicted number of wins, i.e.,, that corresponds with 6 interceptions: 14.002 11.261 15.323 12.135 Using the OLS results and find the residual, i.e., ei, that corresponds with 6 interceptions: 1.865 2.234 3.818 5.196
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 table below shows the number of interceptions (balls caught by opponent team during passing) during the season by seven randomly selected National Football League teams and the number of games those teams won during the season. A simple linear regression model, , is developed with “Wins” being the dependent variable and “Interceptions” as the independent variable.
|
Wins |
Interceptions |
|
3 |
28 |
|
6 |
19 |
|
11 |
16 |
|
14 |
6 |
|
10 |
9 |
|
8 |
25 |
|
8 |
11 |
- Following the Ordinary Least Squares method, find the OLS line: , based on the regression model above:
- b0 = 12.105; b1= -2.0435
- b0 = 12.7676; b1= -1.6896
- b0 = 14.213; b1= -0.346
- b0 = 2.063; b1= -0.115
- Using the OLS results and find the predicted number of wins, i.e.,, that corresponds with 6 interceptions:
- 14.002
- 11.261
- 15.323
- 12.135
- Using the OLS results and find the residual, i.e., ei, that corresponds with 6 interceptions:
- 1.865
- 2.234
- 3.818
- 5.196
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