Consider the following sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2. Linear Quadratic Intercept 13.3087 1.7656 x 0.3392 4.0966 x2 NA -0.2528 R2 0.1317 0.5844 Adjusted R2 0.0232 0.4657 Choose the model with the best fit, and then predict y for x = 4, 8, and 12. ROUND TO TWO DECIMAL PLACES. x Predicted y 4 8 12
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.
Consider the following sample regressions for the linear and quadratic models along with their respective R2 and adjusted R2.
| Linear | Quadratic | |
| Intercept | 13.3087 | 1.7656 |
| x | 0.3392 | 4.0966 |
| x2 | NA | -0.2528 |
| R2 | 0.1317 | 0.5844 |
| Adjusted R2 | 0.0232 | 0.4657 |
Choose the model with the best fit, and then predict y for x = 4, 8, and 12. ROUND TO TWO DECIMAL PLACES.
| x | Predicted y |
| 4 | |
| 8 | |
| 12 |
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