Question

Use the correlations provided here to answer the questions below and the CORRELATIONS questions that follow. X and Y in data set A have correlation 0.123 X and Y in data set B have correlation-0.456 X and Y in data set C have correlation 0.789 X and Y in data set D have correlation-0.098 X and Y in data set E have correlation-0.123 X and Y in data set F have correlation 0.765

Answer 1

The given correlation coefficients indicate different types of relationships between X and Y variables in each data set.

Step-by-step explanation:

Scatter Plot and Linear Regression Analysis

Based on the given correlation coefficients, we can determine the strength and direction of the relationship between variables X and Y in each data set. The positive correlation coefficients (0.789 and 0.765) indicate a strong positive linear relationship, meaning that as X increases, Y also increases. On the other hand, the negative correlation coefficients (-0.456, -0.098, and -0.123) suggest a negative linear relationship, where as X increases, Y decreases. The weak correlation coefficient (0.123) in data set E signifies a weak positive correlation between X and Y.

In summary, the variables X and Y in data sets A, C, and F have strong positive linear relationships, while data sets B, D, and E exhibit negative or weak positive linear relationships.

Answer 2

The question pertains to the correlation coefficient, a measure of the linear relationship between two variables, which can range from -1 to +1. Data sets with correlations close to these extremes suggest strong relationships, while those near zero show weak or no linear relationship. Significant correlations indicate that relationships are not due to random chance, and strong relationships are good for linear regression prediction.

Step-by-step explanation:

The question discusses the concept of the correlation coefficient, which is a statistical measure of the strength and direction of the linear relationship between two variables, denoted as X and Y. Correlation coefficients range from -1 to +1, with values close to +1 indicating a strong positive linear relationship, values close to -1 indicating a strong negative linear relationship, and values around 0 indicating no linear relationship.

In the provided data sets, the correlations vary in strength and direction. For example, data set A with a correlation of 0.123 has a weak positive relationship, meaning that as X increases, Y tends to increase as well, but not very consistently. In contrast, data set B with a correlation of -0.456 has a moderate negative linear relationship, meaning that as X increases, Y tends to decrease, and vice versa. The strength of these relationships can be assessed for significance, which if significant, suggest that the relationship between X and Y is not due to random chance.

Data set C with a correlation of 0.789 and data set F with a correlation of 0.765 both exhibit strong positive relationships, indicating a good fit for predictions using linear regression. Meanwhile, data set D and data set E with correlations of -0.098 and -0.123, respectively, have weak relationships that are likely not useful for prediction purposes.