SST = Ey? – (Ey,)/n, SSR = [Σxy- (Σx)(Σγ)/ n7? Σ- ΣxF/ %3D
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.
Applying the Concepts and Skills
For Exercises,
a. compute SST, SSR, and SSE, using Formula on page 641.
b. compute the coefficient of determination, r2.
c. determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer.
d. state how useful the regression equation appears to be for making predictions.
FORMULA
Computing Formulas for the Sums of Squares
The computing formulas for the three sums of squares are
and SSE= SST-SSR.
Study Time and Score. Following are the data on study time and score for calculus students from Exercise.
| x | 10 | 15 | 12 | 20 | 8.0 | 16 | 14 | 22 |
| y | 92 | 81 | 84 | 74 | 85 | 80 | 84 | 80 |
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