On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that predict a student’s score on the final exam. She estimates the regression model to predict the final exam score using the math test score and number of hours studied per week. A portion of the regression results is shown in the following table. Coefficients Intercept 44.8 Math 0.30 Hours 3.75 (a) Suppose Bella and Ingrid have the same scores on the math test, but Bella studies 2 hours more per week than Ingrid. What is the difference in the final exam scores between the two students? (b) Compute the residual for a student whose math score of 65, studies 5 hours per week, and had a final exam score of 74.
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.
On the first day of class, an economics professor administers a test to gauge the math preparedness of her students. She believes that the performance on this math test and the number of hours studied per week on the course are the primary factors that predict a student’s score on the final exam. She estimates the regression model to predict the final exam score using the math test score and number of hours studied per week. A portion of the regression results is shown in the following table.
|
Coefficients |
|
|
Intercept |
44.8 |
|
Math |
0.30 |
|
Hours |
3.75 |
(a) Suppose Bella and Ingrid have the same scores on the math test, but Bella studies 2 hours more per week than Ingrid. What is the difference in the final exam scores between the two students?
(b) Compute the residual for a student whose math score of 65, studies 5 hours per week, and had a final exam score of 74.
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