When the local harvest starts reaching the market, the price of tomatoes drops from *40 per kg to *10 per kg. Is there any relationship between two variables?
Answer
Yes, there is negative correlation between two variables because these variables move in the opposite direction.
In which correlation, the entire set of independent and dependent variables is simultaneously studied?
Answer
When relationship among three or more than three variables is studied simultaneously, then such correlation is called multiple correlation. In case of such correlation, the entire set of independent and dependent variables is simultaneously studied.
What is the difference between simple and multiple correlation?
Answer
When the relationship between only two variables is studied, it is called 'simple correlation', whereas when the relationship among three or more than three variables is studied simultaneously, it is called 'multiple correlation'.
If the values of $X$ and $Y$ have been ranked and we compute Karl Pearson's coefficient of correlation between ranks of $X$ and $Y$, will this correlation be equal to the value of $r_k$?
Answer
Yes, if the values of $X$ and $Y$ have been ranked and we compute Karl Pearson's coefficient of correlation between ranks of $X$ and $Y$ then this correlation will be equal to the value of $r_k$.
If $\Sigma\text{(X}-\overline{\text{X}})\text{(Y}-\overline{\text{Y}})=90,\Sigma(\text{X}-\overline{\text{X}})^2=144,\Sigma\text{(Y}-\overline{\text{Y}})^2=250$ and N=50, what is karl Person's correlation coeffcient?
Can r lie outside the -1 and 1 range depending on the type of data?
Answer
No, the value of correlation coefficient (r) cannot lie outside the -1 and 1 range depending on the type of data. However, if the value of r lies outside this range, then it implies error in the estimation of correlation coefficient.
A Scatter diagram is a useful technique used for examining visually the form of relationship between the two given variables, without calculating any numerical value.
Give the formula for computation of Karl Pearson's Coefficient of correlation, when deviations are taken from mean.
Answer
Karl Pearson’s Coefficient of Correlation:$\text{r}=\frac{\Sigma\text{xy}}{\sqrt{\Sigma\text{x}^2\times\Sigma\text{y}^2}} \text{ where, x}=\text{X}-\overline{\text{X}},\text{y}=\text{Y}-\overline{\text{Y}}$
Which property of correlation coefficient facilitates it's computation through step deviation method?
Answer
The property of correlation coefficient which facilitates it's computation through step deviation method is that it is neither affected by change in origin nor by change in scale.
No, zero correlation does not imply independence of two variables. If there is zero correlation, it means the two variables (say X and Y) are not correlated and there is no linear relation between them. However, some other type of relation exists between them.
If the amount of change in any one variable tends to bear a constant relation with the amount of change in the other variable, then the correlation is said to be linear correlation.
In case of linear correlation, the relative movement of the two variables can be represented by drawing a straight line on graph paper.