Which of the following statements about correlation are true? Check all that apply. The correlation is scaleless; that is, it doesn't change when the measurement units are changed for either or both of the variables. A positive correlation means that two variables tend to change in the same direction. Correlation is a numerical value between 1.1 and 2. If the correlation between two variables is close to -1, there is a negative linear relationship between the two variables. The correlation indicates the strength and the direction of the linear relationship between two variables. A correlation of 1 indicates that there is little or no linear relationship between the two variables If the correlation between two variables is 0, there is no clear linear relationship between the two variables.

## Answer

**Answers to each part with reasons:**

1. Is true. Change the units, correelation doesn't change

2. True. Meaning all 0 to 1 have +ive correlation

3. False. Correlation ranges from -1 to 1

4. True. 2 variables have opposite movements

5. True. +ive -same direction movements, -ive different direction
movements

6. False. 1 means strong relation

7. True. 0 means no linear relation between variables

The statement "The correlation is scale less; that is, it doesn't change when the measurement units are changed for either or both the variables" is TRUE. The correlation coefficient is calculated as follows: cov(x,y) 1. = var(x)var(y) Thus, correlation is scale less as the units in numerator cancel out with the units in denominator and correlation has no effect with the change in units. The statement “A positive correlation means that two variables tend to change in the same direction” is TRUE. Because the positive correlation means that change in same direction as if one variable increase then other also increases and if one variable decreases then other also decreases. The statement "Correlation is a numerical value between 1.1 and 2” is FALSE. Because the correlation coefficient lies between-1 and 1, that is, -1<r<1. The statement "If the correlation between two variables is close to -1, there is a negative linear relationship between the two variables" is TRUE. Because if the correlation coefficient r=-1 then this shows that there is a negative linear relationship between two variables and if one variable is decreasing then other variable is also decreasing.

The statement "The correlation indicated the strength and the direction of the linear relationship between two variables” is TRUE. As, the correlation coefficient lies between -1<r<1. There is a thumb rule for interpreting the strength of the relationship between two variables by using the absolute value of the r-value. Absolute value ofr Type of relationship 1. r<0.3 None or weak 2. 0.3<r< 0.5 Weak 3. 0.5<r<0.7 Moderate 4. r>0.7 Strong The linear relationship between two variables is absent or weak when the value of r is less than 0.3. The linear relationship between two variables is weak when the value of r lies between 0.3 and 0.5. The linear relationship between two variables is moderate when the value ofr lies between 0.5 and 0.7. The linear relationship between two variables is strong when the value of r is larger than 0.7. When the r-value is close to 0, then variables have no relationship or weak relationship. When the r-value is greater than 0, then it is said to have a positive linear relationship. When the r value is less than 0, then it is said to have a negative linear relationship. The statement "A correlation of 1 indicates that there is little or no linear relationship between the two variables" is FALSE'. Because if the correlation between two variables is 1 then it indicates that there is strong linear relationship between two variables.

The statement "If the correlation between two variables is 0, there is no clear relationship between two variables" is TRUE. If the correlation coefficient between two variables is 0 then it indicates that the variables have no or weak linear relationship between them.

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