Question

for each eppertion, describe the relationship between the variables coefficient. make sure to mention whether there is a strong relationship or weak relati and whether it is a positive relationship or negative relationship. 1 number of steps taken per day and number of kilometers walked per day. ( r = 0.92 ) 2 temperature of a rubber band and distance the rubber band can stretch. ( r = 0.84 ) 3 car weight and distance traveled using a full tank of gas. ( r = - 0.86 ) 4 average fat intake per citizen of a country and average cancer rate of a country. ( r = 0.71 ) 5 score on science exam and number of words written on the essay question. ( r = 0.28 ) 6 average time spent listening to music per day and average time spent watching tv per day ( r = - 0.17 )

Explanation:

1. The correlation coefficient \(r = 0.92\). Since \(|r|=0.92\approx1\) and \(r>0\), there is a strong positive relationship. As the number of steps taken per day increases, the number of kilometers walked per day also increases.
2. The correlation coefficient \(r = 0.84\). Since \(|r| = 0.84\) (close to 1) and \(r>0\), there is a strong positive relationship. As the temperature of a rubber band increases, the distance the rubber band can stretch also increases.
3. The correlation coefficient \(r=-0.86\). Since \(|r| = 0.86\) (close to 1) and \(r<0\), there is a strong negative relationship. As the car weight increases, the distance traveled using a full tank of gas decreases.
4. The correlation coefficient \(r = 0.71\). Since \(|r|=0.71\) (moderate, but closer to 1) and \(r>0\), there is a moderate - strong positive relationship. As the average fat intake per citizen of a country increases, the average cancer rate of a country also tends to increase.
5. The correlation coefficient \(r = 0.28\). Since \(|r|=0.28\) (far from 1) and \(r>0\), there is a weak positive relationship. As the number of words written on the essay question increases, the score on the science exam has a weak tendency to increase.
6. The correlation coefficient \(r=-0.17\). Since \(|r|=0.17\) (far from 1) and \(r<0\), there is a weak negative relationship. As the average time spent listening to music per day increases, the average time spent watching TV per day has a weak tendency to decrease.

Answer:

1. Strong positive relationship.
2. Strong positive relationship.
3. Strong negative relationship.
4. Moderate - strong positive relationship.
5. Weak positive relationship.
6. Weak negative relationship.