Question

The following quote is from a paper on the weight of the bottle as a possible extrinsic cue with which to estimate the price (and quality) of the wine.
The weight of the wine bottles was positively correlated (r=0.13) with the price of the wine.

1. Does the value Of the correlation coefficient indicate that the relationship is weak, moderate, or strong?

a. Weak
b. Moderate
c. Strong

2. What is the value of r^2? Write a sentence that gives an interpretation of this value.

Answer 1

Answer:

1. a. Weak

2. r^2=0.0169

The variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%.

Step-by-step explanation:

The correlation between the weight of the wine bottles and the price of the wine is r=0.13.

The values for r goes from r=-1, where a perfect negative correlation to r=1 for a perfect positive correlation. The value r=0 indicates no correlation at all.

Then, a value of r close to 0 indicates very weak correlation between the two variables.

The value for r^2 in this case is:

$r^2=0.13^2=0.0169$

The value of r2 can be interpreted as the proportion of the variation in the dependant variable explained by the independent vairable. In this case, the variation in the price of the wine explained by the variation in the weight of the bottle is 1.69%, which is very close to 0.