The diagram presents three scatter plots, each representing a different type of correlation between two variables $X$ and $Y$. Let's identify the type of correlation shown in each case:

1. Plot (a): Positive Correlation

   • In this plot, as the value of $X$ increases, the value of $Y$ also increases. The points show an upward trend from left to right. This is an example of a positive correlation, where higher values of one variable are associated with higher values of the other variable.

2. Plot (b): Negative Correlation

   • In this plot, as the value of $X$ increases, the value of $Y$ decreases. The points show a downward trend from left to right. This is an example of a negative correlation, where higher values of one variable are associated with lower values of the other variable.

3. Plot (c): No Correlation

   • In this plot, the points are scattered randomly with no discernible pattern or trend. The values of $X$ and $Y$ do not show any clear relationship. This represents no correlation between the two variables.

Would you like more details on correlation types or how they are measured?

Questions:

1. How can you calculate the strength of correlation numerically?
2. What statistical methods are used to verify the correlation between two variables?
3. Can you explain the difference between linear and nonlinear correlation?
4. What role does the Pearson correlation coefficient play in determining correlation?
5. How would outliers affect the correlation in a scatter plot?

Tip:

The strength of a correlation is often measured by the correlation coefficient, which ranges from -1 (perfect negative correlation) to 1 (perfect positive correlation), with 0 indicating no correlation.