Consider the following to answer the question(s) below:
A consumer research group investigating the relationship between the price of meat (per kilogram) and the fat content (grams) gathered data that produced the following scatterplot.
-A perfect correlation between two variables will always produce which of the following?
A) a correlation coefficient of -1.0
B) a scatterplot with a pattern running from lower left to upper right
C) a correlation coefficient of 1.0
D) a scatterplot where all points lie on a single straight line
E) a scatterplot with a pattern running from upper left to lower right

Question

Consider the following to answer the question(s) below:
A consumer research group investigating the relationship between the price of meat (per kilogram) and the fat content (grams) gathered data that produced the following scatterplot. 
-A perfect correlation between two variables will always produce which of the following?
A) a correlation coefficient of -1.0 
B) a scatterplot with a pattern running from lower left to upper right 
C) a correlation coefficient of 1.0 
D) a scatterplot where all points lie on a single straight line 
E) a scatterplot with a pattern running from upper left to lower right

Quizplus · Accepted Answer

A perfect correlation between two variables means that there is a deterministic relationship between them, with no variability or random error. This implies that all the data points fall on a single straight line in the scatterplot, which corresponds to a correlation coefficient of either -1.0 or 1.0, depending on the direction of the relationship (positive or negative). Therefore, the correct answer is D, as all the other options do not accurately reflect a perfect correlation. Option A is incorrect as a negative correlation produces a pattern from upper left to lower right, not lower left to upper right. Option B describes a positive correlation, but it is not necessarily perfect. Option C is correct but incomplete, as a perfect correlation can be positive or negative.

Consider the Following to Answer the Question(s) Below