## Introduction

In statistics, correlation is used to determine the relationship between two variables. It measures the strength of the relationship between the variables and the direction of the relationship. The correlation coefficient, denoted by r, ranges from -1 to 1. When r is close to 1, it indicates a strong positive relationship between the variables. In this article, we will explore scatterplots that have a correlation coefficient closest to r 1.

## Scatterplots with Positive Correlation

Scatterplots are graphs that display the relationship between two variables. When the variables are positively correlated, the points on the scatterplot tend to form a straight line that goes from the bottom left to the top right of the graph. The closer the points are to the line, the stronger the correlation is.

### Example 1: Height and Weight

One example of a scatterplot with a correlation coefficient closest to r 1 is the relationship between height and weight. Taller people tend to weigh more, so the points on the scatterplot form a straight line that goes from the bottom left to the top right. The correlation coefficient for this scatterplot is likely to be very close to 1.

### Example 2: Education and Income

Another example of a scatterplot with a correlation coefficient closest to r 1 is the relationship between education and income. People with higher levels of education tend to have higher incomes, so the points on the scatterplot form a straight line that goes from the bottom left to the top right. The correlation coefficient for this scatterplot is also likely to be very close to 1.

## Scatterplots with Negative Correlation

When the variables are negatively correlated, the points on the scatterplot tend to form a straight line that goes from the top left to the bottom right of the graph. The closer the points are to the line, the stronger the correlation is.

### Example 1: Temperature and Sales

One example of a scatterplot with a correlation coefficient closest to r 1 is the relationship between temperature and sales. In general, sales tend to increase when the temperature is moderate. However, when the temperature is too hot or too cold, sales tend to decrease. The points on the scatterplot form a straight line that goes from the top left to the bottom right. The correlation coefficient for this scatterplot is likely to be very close to -1.

### Example 2: Age and Reaction Time

Another example of a scatterplot with a correlation coefficient closest to r 1 is the relationship between age and reaction time. As people get older, their reaction time tends to slow down. The points on the scatterplot form a straight line that goes from the top left to the bottom right. The correlation coefficient for this scatterplot is also likely to be very close to -1.

## Scatterplots with Weak Correlation

When the variables are weakly correlated, the points on the scatterplot do not form a straight line. The correlation coefficient is closer to 0, indicating a weak relationship between the variables.

### Example 1: Height and Shoe Size

One example of a scatterplot with a weak correlation is the relationship between height and shoe size. While taller people tend to have larger shoe sizes, the relationship is not strong. The points on the scatterplot are scattered and do not form a straight line. The correlation coefficient for this scatterplot is likely to be close to 0.

### Example 2: Age and Favorite Color

Another example of a scatterplot with a weak correlation is the relationship between age and favorite color. There is no clear relationship between the two variables, so the points on the scatterplot are scattered and do not form a straight line. The correlation coefficient for this scatterplot is also likely to be close to 0.

## Conclusion

In conclusion, the scatterplots that have a correlation coefficient closest to r 1 are those that have a strong positive or negative correlation. These scatterplots form a straight line that goes from the bottom left to the top right or from the top left to the bottom right. Scatterplots with weak correlation do not form a straight line and have a correlation coefficient close to 0. By understanding these concepts, you can better interpret scatterplots and the relationship between variables.