Number of samples = 6

Correlation coefficient = 0.9863

R^{2} = 0.9729

GENERATE WORK

GENERATE WORK

**Input Data : **

Data set x = 3, 8, 10, 17, 24, 27

Data set y = 2, 8, 10, 13, 18, 20

Total number of elements = 6

**Objective :**

Find what is correlation coefficient for given input data?

**Solution :**

Correlation = (3 - 14.8333)(2 - 11.8333) + ( 8 - 14.8333)( 8 - 11.8333) + ( 10 - 14.8333)( 10 - 11.8333) + ( 17 - 14.8333)( 13 - 11.8333) + ( 24 - 14.8333)( 18 - 11.8333) + ( 27 - 14.8333)( 20 - 11.8333) (6 - 1) x 9.4534 x 6.6458 = (-11.8333 x -9.8333) + (-6.8333 x -3.8333) + (-4.8333 x -1.8333) + (2.1667 x 1.1667) + (9.1667 x 6.1667) + (12.1667 x 8.1667)(5) x 9.4534 x 6.6458

= (116.3604) + (26.1941) + (8.8609) + (2.5279) + (56.5283) + (99.3618)(314.1269)

= 309.8333(314.1269)

Correlation = 0.9863

R² = (Correlation)²

= (0.9863)²

R² = 0.9728

** R Squared Calculator** is an online statistics tool for data analysis programmed to predict the future outcome with respect to the proportion of variability in the other data set. The coefficient of equation R^2 as an overall summary of the effectiveness of a least squares equation.

R^2 is the coefficient of determination that shows the relation between dependent variable and the other independent variables. The possible future outcomes can be calculated from the R squared value. This R squared value summarizes the shape of the single future failure outcome independently, but it is also useful to compare the shape of a collection of failures with different combinations of data sets. Generally, the coefficient of determination denoted by R^2 is the most common measure of the overall model fitting procedure of a regression used for prediction and forecasting.

The R square value can be mathematically derived from the below formula

The collection of tools employs the study of methods and procedures used for gathering, organizing, and analyzing data to understand theory of Probability and Statistics. The set of ideas which is intended to offer the way for making scientific implication from such resulting summarized data. In many applications it is necessary to calculate the future possible outcome, where this online R squared value calculator can assist you to effortlessly make your calculation for the given data sets.