Which of the following pairs of variables is likely to have a positive correlation? Select all that apply.
a. The number of miles run and the number of calories burned
b. Years of education and salary
c. The square footage of a home and its price
d. The speed of a car and the time to its destination
e. A person's height and their favorite color
Explain??
Think about what the question is asking you and then look at the answers. A positive correlation between two variables means that as the independent variable increases, the dependent variable also increases.
A)Do the number of miles run and the number of calories burned have a positive correlation? They likely do since running more uses energy and that energy burns the calories, especially to a person who weighs more.
B) Do the years of education and salary have a positive correlation? They likely do since someone with more education has more opportunities to obtain certain jobs that are more high-paying such as an engineer.
C) Do the square footage of a home and its price have a positive correlation? They likely do since the bigger the living space, it's generally more expensive to afford
D) Do the speed of a car and the time to its destination have a positive correlation? They don't because as you go faster, your time to your destination decreases, which logically makes sense since speed=distance/time
E) Do a person's height and their favorite color have a positive correlation? They don't because they are completely different topics. A short person or tall person can have any color as their favorite color.
Therefore, A, B, and C, are correct
a. The number of miles run and the number of calories burned - It is likely that there is a positive correlation between the number of miles run and the number of calories burned. As you run more miles, you typically burn more calories.
b. Years of education and salary - It is also likely that there is a positive correlation between years of education and salary. Generally, the more education someone has, the higher their earning potential.
c. The square footage of a home and its price - Similarly, the square footage of a home and its price are likely to have a positive correlation. In general, larger homes tend to have higher prices.
d. The speed of a car and the time to its destination - There is likely a negative correlation between the speed of a car and the time to its destination. As the car's speed increases, the time to reach the destination decreases.
e. A person's height and their favorite color - Sorry, but there is no logical correlation between a person's height and their favorite color. Unless, of course, tall people have a tendency to favor colors closer to the sky. But that's just speculation.
The pairs of variables that are likely to have a positive correlation are:
a. The number of miles run and the number of calories burned: As the number of miles run increases, the number of calories burned also tends to increase. This is because running more miles requires more energy expenditure, resulting in more calories burned.
b. Years of education and salary: Typically, the level of education is positively related to salary. As a person acquires more years of education, they tend to gain more knowledge and skills, making them more qualified for higher-paying jobs.
c. The square footage of a home and its price: In general, larger homes tend to have higher prices. This is because more square footage usually means more living space, amenities, and potentially a more desirable location, resulting in higher market value.
d. The speed of a car and the time to its destination: As the speed of a car increases, the time it takes to reach its destination tends to decrease. This is due to the basic relationship between speed and time — the faster the car travels, the more quickly it can cover a given distance.
The pair of variables that is not likely to have a positive correlation is:
e. A person's height and their favorite color: There is no inherent relationship between a person's height and their favorite color. Height and color preference are independent variables and are not expected to have a positive correlation.
To determine which pairs of variables are likely to have a positive correlation, we need to understand what a positive correlation means. A positive correlation means that as one variable increases, the other variable also tends to increase, and vice versa. In other words, the two variables tend to move in the same direction.
a. The number of miles run and the number of calories burned: These two variables are likely to have a positive correlation. As the number of miles run increases, the number of calories burned is also expected to increase.
b. Years of education and salary: These two variables are also likely to have a positive correlation. Typically, as a person's level of education increases, their salary tends to increase too.
c. The square footage of a home and its price: These two variables are likely to have a positive correlation. As the square footage of a home increases, its price is generally expected to increase as well.
d. The speed of a car and the time to its destination: These two variables do not have a positive correlation. As the speed of a car increases, the time to its destination actually decreases.
e. A person's height and their favorite color: These two variables do not have any logical relationship, so they are not likely to have a positive correlation.
In summary, the pairs of variables that are likely to have a positive correlation are:
a. The number of miles run and the number of calories burned
b. Years of education and salary
c. The square footage of a home and its price