A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 10 students are shown in the table below. Student 1 2 3 4 5 6 7 8 9 10 Score 58 71 29 27 39 80 51 64 30 78 Grade 98 61 95 61 62 78 90 94 72 81 Find the following: (a) The correlation coefficient: r= (b) The least squares line: y^= (c) The predicted grade for the seventh student:
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 study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 10 students are shown in the table below.
| Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Score | 58 | 71 | 29 | 27 | 39 | 80 | 51 | 64 | 30 | 78 |
| Grade | 98 | 61 | 95 | 61 | 62 | 78 | 90 | 94 | 72 | 81 |
Find the following:
(a) The
(b) The least squares line: y^=
(c) The predicted grade for the seventh student:
(d) The residual for the seventh student:
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