Question

A scatter diagram of the data is shown. What type of relationship appears to exist between A and B?

Answer 1

The scatter diagram suggests a positive linear relationship between variables A and B.

Step-by-step explanation:

The scatter diagram visually indicates the nature of the relationship between variables A and B. In a positive linear relationship, as the value of one variable (A) increases, the value of the other variable (B) also tends to increase in a consistent manner.

This is reflected in the scatter plot by a trend where data points cluster in a manner that forms an upward-sloping line. The strength and direction of this relationship can be quantified using correlation coefficients.

To further support this observation, a correlation coefficient such as the Pearson correlation coefficient (r) can be calculated. If the calculated value of r is close to +1, it confirms a strong positive linear relationship. The formula for the Pearson correlation coefficient is:

`\[ r = \frac{\sum{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sqrt{\sum{(X_i - \bar{X})^2} \sum{(Y_i - \bar{Y})^2}}} \]`

Here,
`\(X_i\)`and
`\(Y_i\)` are individual data points, and
`\(\bar{X}\)`and
`\(\bar{Y}\)` are the means of variables A and B, respectively. A positive value of r indicates a positive correlation.

In summary, by analyzing the scatter diagram and calculating the correlation coefficient, one can conclude whether a positive linear relationship exists between variables A and B, providing a quantitative measure of the strength and direction of the association.