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

Quizplus · Accepted Answer

The value of R2 only indicates the proportion of the total variation in the dependent variable (y) that is explained by the independent variable (x). It does not tell us the direction of the relationship between the two variables. The correlation coefficient (r) measures the strength and direction of the linear relationship between x and y. The possible values of r range from -1 to +1, indicating negative or positive correlation, respectively. Since R2 = r2, we can obtain the correlation coefficient by taking the square root of R2. Therefore, the correlation coefficient can be either 0.8851 or -0.8851.

Consider the Following to Answer the Question(s) Below