Q:

Which relationships would most likely be causal? Check all that apply. A.) a positive correlation between time spent exercising and the number of calories burned B.) a negative correlation between temperature and coat sales C.)a positive correlation between time spent practicing free throws and free throw percentage D.)a positive correlation between time spent on the phone with friends and the number of friends E.) a negative correlation between temperature and the number of speeding tickets

Accepted Solution

A:
Calories burned positively depends on exercise time,coat sales negatively depends on temperature and free throw percentage positively depends on free throws. The option A, B and C shows the casual relationship.What is correlation between variables?When there is a statically relationship exist between two or more variable, then they are said to be in correlation.Correlation coefficient is used to calculate that how strong the relationship is between the two variables.Types of correlation- Positive correlation coefficient- When there is the value of correlation coefficient is positive, then the value of one variable is increases with increase in other variable.Negative correlation coefficient- When there is the value of correlation coefficient is negative, then the value of one variable is decreases with increase in other variable.Lets check all the options-A.) A positive correlation between time spent exercising and the number of calories burned- The more exercise by a person results in more calories burned. Thus one variable is increasing with increase in other, which indicates positive relationship. Thus this shows casual relationship.B.) A negative correlation between temperature and coat sales-The more in the increase of temperature results in less the sales of coats. Thus one variable is decreasing with increase in other, which indicates negative relationship. Thus this option shows casual relationship.C.) A positive correlation between time spent practicing free throws and free throw percentage-The more in the increase of time spent practicing free throws results in more the  free throw percentage. Thus one variable is increasing with increase in other, which indicates positive relationship. Thus this option shows casual relationship.D.)A positive correlation between time spent on the phone with friends and the number of friends- Number of friends does not depends on the time spent on the phone call with friend.E.) A negative correlation between temperature and the number of speeding tickets- Temperature does not effect of fasten the speeding of tickets.Thus Calories burned positively depends on exercise time,coat sales negatively depends on temperature and free throw percentage positively depends on free throws. Hence, the option A, B and C shows the casual relationship.Learn more about the correlation coefficient here;