What is If correlation between weight and heights are very strong what will be the correlation coefficient ? and explain in detail?
Ans. is 'a' i.e., +1 o A correlation simply expresses the strength and direction of the relationship between two variables in terms of a correlation coefficient, signified by `r'. o Values of r varies from -1 to +1.; o The strength of the relationship is indicated by the size of the coefficient , whereas its direction is indicated by the sign(+ or -) o A plus sign (+) means : That there is a positive correlation between the two variables - high values of one variable (such as salt intake ) are associated with high value of the other variable ( such as blood pressure) i.e salt intake is directly propoional to blood pressure. o A negative sign (-) means : That there is a negative correlation between the two variables - high values of one variables (such as cigarette consumption ) are associated with low values of the other ( such as life expectancy). Cigarette consumption is inversely propoional to life expectancy o If there is a perfect linear relationship between the two variables so that it is possible to know the exact value of one variable from the knowledge of other variable, the correlation coefficient ( r) will be exactly + or - 1.00 ( +1 or -1 ). o If there is absolutely no relationship between the two variables so that it is impossible to know anything about one variable on the basis of knowledge of the other variable. Then the coefficient will be 0. Strength of correlation o The strength of linear relationship between two random variables X and Y is based on the value of correlation coefficient and is often summarized according to the following guidelines:- For Positive Correlation For negative correlation Interpretation r<0. 30 - 0.30 r very weak linear relationship 0.30 5 r < 0.50 - 0.50 < r 5 - 0.30 weak linear relationship 0.50 _. r < or 0.80 - 0.80 <r - 0.50 moderate linear relationship 0.80 5..r< 0.90 - 0.90 <r- 0.80 strong linear relationship r 0.90 1.5.-0.90 very strong linear relationship o If you have difficulty in interpreting above table, I am giving in very simple language:- A. Positive Correlation i) Correlation coefficient less than 0.30 Very weak positive correlation. ii) Correlation coefficient 0.30 to 0.49 --) Weak Positive correlation iii) Correlation coefficient 0.50 to 0.79 Moderate Positive correlation iv) Correlation coefficient 0.80 to 0.89 --)Strong Positive correlation v) Correlation Coefficient equal to or greater than 0.90--> very strong positive correlation. B. Negative Correlation i) Correlation coefficient more than - 0.30 Very weak negative correlation ii) Correlation coefficient - 0.30 to - 0.497-> Weak negative correlation iii) Correlation coefficient - 0.50 to - 0.79 --> Moderate negative correlation iv) Correlation coefficient - 0.80 to - 0.89 Strong negative correlation. v) Correlation coefficient equal or less then - 0.90 --> very strong negative correlation Note: you should keep in mind that for negative values, more means towards more positive side and less means towards more negative side. For example; if we are saying, more than - 0.30, that mean - 0.29, - 0.28, - 0.27 .... so on; and if we are saying less than - 0.90 that means - 0.91, - 0.92 .... so on.