Q: Using the Student Grades data posed below this question, apply the Excel Regression tool using the midterm grade as the independent variable and the final exam grade as the dependent variable. Interpret all key regression results, hypothesis tests, and confidence intervals in the output. The hypothesis test and confidence interval you should interpret are for the slope. Include the Excel data, output, and your interpretations. Also interpret the standard error of the estimates and the R^2 coefficient. Student Grades Student Midterm Final Exam 1 76 65 2 84 90 3 79 68 4 88 84 5 76 61 6 66 79 7 77 73 8 94 93 9 66 60 10 92 86 11 80 53 12 87 83 13 86 55 14 63 72 15 92 87 16 75 89 17 69 81 18 92 94 19 79 78 20 60 71 21 68 84 22 71 74 23 61 74 24 68 54 25 76 94 26 72 79 27 99 89 28 58 53 29 82 78 30 72 82 31 77 69 32 95 98 33 72 93 34 71 80 35 72 82 36 96 96 37 72 61 38 89 84 39 94 97 40 85 89 41 60 72 42 66 93 43 96 84 44 83 87 45 88 99 46 92 97 47 78 92 48 85 93 49 91 78 50 74 82 51 96 99 52 80 72 53 62 79 54 70 75 55 87 90 56 89 95
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.
Q: Using the Student Grades data posed below this question, apply the Excel Regression tool using the midterm grade as the independent variable and the final exam grade as the dependent variable. Interpret all key regression results, hypothesis tests, and confidence intervals in the output.
The hypothesis test and confidence interval you should interpret are for the slope. Include the Excel data, output, and your interpretations. Also interpret the standard error of the estimates and the R^2 coefficient.
| Student Grades | ||
| Student | Midterm | Final Exam |
| 1 | 76 | 65 |
| 2 | 84 | 90 |
| 3 | 79 | 68 |
| 4 | 88 | 84 |
| 5 | 76 | 61 |
| 6 | 66 | 79 |
| 7 | 77 | 73 |
| 8 | 94 | 93 |
| 9 | 66 | 60 |
| 10 | 92 | 86 |
| 11 | 80 | 53 |
| 12 | 87 | 83 |
| 13 | 86 | 55 |
| 14 | 63 | 72 |
| 15 | 92 | 87 |
| 16 | 75 | 89 |
| 17 | 69 | 81 |
| 18 | 92 | 94 |
| 19 | 79 | 78 |
| 20 | 60 | 71 |
| 21 | 68 | 84 |
| 22 | 71 | 74 |
| 23 | 61 | 74 |
| 24 | 68 | 54 |
| 25 | 76 | 94 |
| 26 | 72 | 79 |
| 27 | 99 | 89 |
| 28 | 58 | 53 |
| 29 | 82 | 78 |
| 30 | 72 | 82 |
| 31 | 77 | 69 |
| 32 | 95 | 98 |
| 33 | 72 | 93 |
| 34 | 71 | 80 |
| 35 | 72 | 82 |
| 36 | 96 | 96 |
| 37 | 72 | 61 |
| 38 | 89 | 84 |
| 39 | 94 | 97 |
| 40 | 85 | 89 |
| 41 | 60 | 72 |
| 42 | 66 | 93 |
| 43 | 96 | 84 |
| 44 | 83 | 87 |
| 45 | 88 | 99 |
| 46 | 92 | 97 |
| 47 | 78 | 92 |
| 48 | 85 | 93 |
| 49 | 91 | 78 |
| 50 | 74 | 82 |
| 51 | 96 | 99 |
| 52 | 80 | 72 |
| 53 | 62 | 79 |
| 54 | 70 | 75 |
| 55 | 87 | 90 |
| 56 | 89 | 95 |
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