You are testing the null hypothesis that there is no linear relationship between two​ variables, X and Y. From your sample of n=12, you determine that r=0.5.   a. What is the value of tSTAT​? b. At the α=0.05 level of​ significance, what are the critical​ values? c. Based on your answers to​ (a) and​ (b), what statistical decision should you​ make?     tSTAT=? ​(Round to four decimal places as​ needed.)   b. The lower critical value is=? ​(Round to four decimal places as​ needed.)   The upper critical value is=? ​(Round to four decimal places as​ needed.)   c. What statistical decision should you​ make?     A. Since tSTAT is greater than the upper critical value​, do not reject H0.   B. Since tSTAT is greater than the upper critical value​, reject H0.   C. Since tSTAT is between the critical values​, do not reject H0.   D. Since tSTAT is between the critical values​, reject

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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.