Given the following data   X= additional number of               Y= Grade improvement since last exam studying hours since last exam 2                                                                    5 4                                                                   6 5                                                                   8 5                                                                  10 7                                                                  11 8                                                                 12 10                                                               13 12                                                               14 12                                                               15 9                                                                 12   a.     Draw a scatter diagram and speculate on the direction linear relationship between the two variables (in complete sentence)...Clearly label the 2 axes...   b.     Find the coefficient of correlation (r) and Comment on it (Please use complete sentences to respond) c.     Compute the coefficient of determination(R2) and tell us what it means   d.     Is the correlation significant at alpha = 0.05? Justify your answer? What does it mean?   e.     Find the equation of the regression line and make an interpolation of the value of Grade improvement since last exam if 11 additional hours of studying since last exam was observed. y = mx+b or y = b1x + b0

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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.