Consider the following to answer the question(s) below:
A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many kilograms of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below.

-A regression on a pair of variables, x and y, results in the value of R2 equal to 0.7834. Which of the following statements is true?
A) The correlation between x and y must be 0.7834.
B) The correlation between x and y must be -0.8851.
C) The correlation between x and y must be -0.7834.
D) The correlation between x and y must be either 0.8851 or -0.8851.
E) The correlation between x and y must be 0.8851.

Question

Consider the following to answer the question(s) below:
A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many kilograms of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below.
  
-A regression on a pair of variables, x and y, results in the value of R2 equal to 0.7834. Which of the following statements is true?
A) The correlation between x and y must be 0.7834. 
B) The correlation between x and y must be -0.8851. 
C) The correlation between x and y must be -0.7834. 
D) The correlation between x and y must be either 0.8851 or -0.8851. 
E) The correlation between x and y must be 0.8851.

Quizplus · Accepted Answer

The R2 value represents the proportion of the total variation in the y-variable that can be explained by the variation in the x-variable. The sign of the correlation coefficient can be positive or negative, depending on the direction of the linear relationship between the two variables. Since the R2 value is positive, we know the correlation must be either positive or negative. However, we cannot determine the direction of the correlation just by looking at the R2 value. Therefore, the correlation between x and y must be either 0.8851 or -0.8851.

Consider the Following to Answer the Question(s) Below