The accompanying technology output was obtained by using the paired data consisting of foot lengths​ (cm) and heights​ (cm) of a sample of 40 people. Along with the paired sample​ data, the technology was also given a foot length of 23.5 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 23.5 ​cm, what is the single value that is the best predicted height for that​ person?   The single value that is the best predicted height is _____cm.     The regression equation is Height=50.8+3.20 Foot Length   Predictor Coef SE Coef T P Constant 50.82 11.65 4.36 0.000 Foot Length 3.1982 0.4903 6.52 0.000   S=5.50372 ​R-Sq=71.7​% ​R-Sq(adj)=71.0​%   Predicted Values for New Observations   New Obs Fit SE Fit ​95% CI ​95% PI 1 125.978 1.744 ​(121.356​, 130.600​) ​(114.681​, 137.275​)   Values of Predictors for New Observations   New Obs Foot Length 1 23.5

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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.