Question

How would you describe the relationship between the two

variables?
a) strong?
b) weak?
c) moderate? and is it linear or non linear or no relationship

Answer 1

To describe the relationship between two variables, a scatter plot and the correlation coefficient are used to determine the strength, direction and form of the relationship. A strong negative linear relationship means that the scatter plot shows a downward trend, and the correlation coefficient will be close to -1.

Step-by-step explanation:

To describe the relationship between two variables, one can use a scatter plot to visually assess the trend and a statistical measure known as the correlation coefficient to quantify the strength and direction of the relationship. The independent variable is the one that is hypothesized to influence the other variable, while the dependent variable is the one that is expected to be affected.

In the case of a strong relationship, the scatter plot will show points that lie close to a straight line, either upward (positive) or downward (negative) sloping. In a scenario where the X and Y variables have a strong negative linear relationship, this indicates that as the value of X increases, the value of Y tends to decrease and vice versa. To analyze this, one would:

1. Draw a scatter plot.
2. Calculate the least-squares line (line of best fit) using the formula ŵ = a + bx.
3. Find the correlation coefficient, which if close to -1 implies a strong negative linear relationship.

The significance of the correlation coefficient indicates whether the observed relationship is statistically significant and not due to random chance. If the relationship is linear, a line of best fit can be used to predict values of the dependent variable based on the independent variable.