Applying the Concepts and SkillsIn Exercises, we repeat data from exercises in Section 14.2. For each exercise here,a. obtain the linear correlation coefficient.b. interpret the value of r in terms of the linear relationship between the two variables in question.c. discuss the graphical interpretation of the value of r and verify that it is consistent with the graph you obtained in the corresponding exercise in Section 14.2.d. square r and compare the result with the value of the coefficient of determination you obtained in the corresponding exercise in Section 14.3.Study Time and Score. Following are the data on study time and score for calculus students from Exercises. x 10 15 12 20 8 16 14 22 y 92 81 84 74 85 80 84 80
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
In Exercises, we repeat data from exercises in Section 14.2. For each exercise here,
a. obtain the linear
b. interpret the value of r in terms of the linear relationship between the two variables in question.
c. discuss the graphical interpretation of the value of r and verify that it is consistent with the graph you obtained in the corresponding exercise in Section 14.2.
d. square r and compare the result with the value of the coefficient of determination you obtained in the corresponding exercise in Section 14.3.
Study Time and Score. Following are the data on study time and score for calculus students from Exercises.
| x | 10 | 15 | 12 | 20 | 8 | 16 | 14 | 22 |
| y | 92 | 81 | 84 | 74 | 85 | 80 | 84 | 80 |
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