A statistics instructor wanted to see if it was possible to predict final exam scores based off of the students' midterm exam scores. Here is an analysis of what she found. Final Exam Grades 90 R2 51.12% Se 6.37 80 70 Variable Coefficient Intercept 33.4 60 Midterm Exam Score (slope) 0.58 60 70 80 Midterm Exam Grades 90 (a) Write the equation of the regression line based on this data. (b) If Mike scored a 92 on the midterm, what does this model predict his final exam grade will be? (c) Mike got an 82 on the final. How big or small is his residual (find actual value)? (d) In this context, what does it mean to say a student has a negative residual? (e) Interpret the slope in this context. (f) Interpret the intercept in this context. (g) What fraction of variability is not accounted for by this model (give value)?

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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.