Which linear relationship has a stronger correlation, a relationship with r=−0.84 or a relationship with r=0.72? Explain.(1 point)
Responses
A. The linear relationship with r=−0.84 because the absolute value of r is closer to 1.
B. The linear relationship with r=−0.84 because it is the closest to −1.
C. The linear relationship with r=0.72 because it is the closest to 1.
D. The linear relationship with r=0.72 because it has the smallest absolute value.
B. The linear relationship with r=−0.84 because it is the closest to −1.
The strength of the correlation between two variables is determined by the absolute value of the correlation coefficient (r), with values closer to 1 indicating a stronger relationship. In this case, r=−0.84 is closer to −1 than r=0.72 is to 1, indicating a stronger negative correlation between the variables.
A biology student is investigating the claim that the temperature can be predicted by counting cricket chirps. He collected some data and found that the correlation coefficient is 0.82. What kind of correlation exists between the variables?(1 point)
Responses
A. a weak positive correlation
B. a strong positive correlation
C. a weak negative correlation
D. a strong negative correlation
B. a strong positive correlation
A correlation coefficient of 0.82 indicates a strong positive correlation between the two variables.
A researcher monitoring the power from the solar panels on a Mars lander has developed a regression model for the available power output in watts, P, against the number of days since landing, d, to help predict the change in power due to dust accumulation. The correlation coefficient is −0.92. What kind of correlation exists between the variables?(1 point)
Responses
A. a strong positive correlation
B. a weak negative correlation
C. a strong negative correlation
D. a weak positive correlation
C. a strong negative correlation
A correlation coefficient of −0.92 indicates a strong negative correlation between the two variables.
A real estate agent has developed a linear model for the price of a house, P, in dollars in terms of the area, A, in square feet for the homes in a certain neighborhood. The correlation coefficient for the relationship is 0.42. What kind of correlation exists between the variables?(1 point)
Responses
A. a weak negative correlation
B. a strong negative correlation
C. a weak positive correlation
D. a strong positive correlation
C. a weak positive correlation
A correlation coefficient of 0.42 indicates a weak positive correlation between the two variables.