Question

Suppose x and y have correlation of -0.85. Which statement is false?

a. The slope of the regression with x and y would be negative
b. A scatter plot of the data displays and upward-sloping pattern when moving from left to right
c. As x increases, y tends to decrease
d. The variables x and y are strongly related

Answer 1

The false statement is 'A scatter plot of the data displays an upward-sloping pattern when moving from left to right.' With a correlation of -0.85, which indicates a strong negative relationship, the scatter plot would display a downward-sloping pattern as x increases.

Step-by-step explanation:

If we suppose x and y have a correlation of -0.85, we need to identify which statement is false:

• The slope of the regression with x and y would be negative.
• A scatter plot of the data displays an upward-sloping pattern when moving from left to right.
• As x increases, y tends to decrease.
• The variables x and y are strongly related.

A negative correlation value, such as -0.85, indicates a strong negative relationship between x and y. This means:

• The slope of the regression line would indeed be negative.
• As x increases, y tends to decrease.
• x and y are strongly related, given the close value to -1.0.

Thus, the false statement is:

A scatter plot of the data displays an upward-sloping pattern when moving from left to right.

In fact, with a negative correlation, the pattern would be a downward slope as x increases. Hence, the correct pattern for this strong negative correlation would be a downward-sloping line on the scatter plot.