A car manufacturer collects data on the number of gallons of gasoline left in the gas tank after driving for different numbers of miles. The manufacturer creates a scatter plot of the data and determines that the correlation coefficient is −0.92.
Select each true statement based on this correlation coefficient.
A. There is a linear correlation between the number of miles driven and the gallons of gasoline left in the tank.
B. There is no correlation between the number of miles driven and the gallons of gasoline left in the tank.
C. There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank.
D. There is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.
E. There is a weak correlation between the number of miles driven and the gallons of gasoline left in the tank.
A. Cars have a miles per gallon (mpg) coefficient.
C. -0.96 is nearly -1
D. The higher the miles driven, the less the gas left.
So yeah, A, C & D.
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To determine the correct statements based on the correlation coefficient of -0.92, we need to understand how the correlation coefficient measures the linear relationship between two variables.
The correlation coefficient, often denoted as "r," ranges from -1 to 1. A value of 1 indicates a perfect positive linear relationship, meaning that as one variable increases, the other variable also increases at a consistent rate. A value of -1 indicates a perfect negative linear relationship, where as one variable increases, the other variable decreases at a consistent rate. A value of 0 indicates no linear relationship or correlation between the variables.
Given that the correlation coefficient in this scenario is -0.92, we can make the following conclusions:
A. False: There is a linear correlation between the number of miles driven and the gallons of gasoline left in the tank. A correlation coefficient of -0.92 indicates a nonlinear relationship.
B. False: There is a correlation between the number of miles driven and the gallons of gasoline left in the tank. A correlation coefficient of -0.92 suggests a significant relationship.
C. True: There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank. A correlation coefficient of -0.92 indicates a strong negative linear relationship.
D. True: There is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank. The negative correlation is evident from the negative correlation coefficient value of -0.92.
E. False: There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank. A correlation coefficient of -0.92 indicates a strong negative linear relationship, not a weak one.
Therefore, the correct statements are:
C. There is a strong correlation between the number of miles driven and the gallons of gasoline left in the tank.
D. There is a negative correlation between the number of miles driven and the gallons of gasoline left in the tank.