Question

Give examples of two variables that have a perfect positive linear correlation and two variables that have a perfect negative linear correlation.

Answer 1

Two examples of variables with a perfect positive linear correlation are distance traveled and fuel consumed by a car with constant fuel efficiency. Two variables with a perfect negative linear correlation include temperature in degrees Fahrenheit and the volume of a fixed amount of gas at constant pressure. Correlation coefficients of +1 and -1 represent perfect positive and negative linear correlations, respectively.

Step-by-step explanation:

When examining relationships between variables, it's important to distinguish between different types of correlations. A perfect positive linear correlation occurs when two variables increase together at a constant rate. For example, the relationship between the distance traveled and the amount of fuel consumed by a car that has a constant fuel efficiency is a perfect positive correlation. As the distance increases, so does the fuel consumed.

In contrast, a perfect negative linear correlation happens when one variable increases as the other decreases at a constant rate. An illustration of this would be the relationship between the temperature in degrees Fahrenheit and the amount of gas left in a fixed volume of a gas at constant pressure: as the temperature decreases, the volume of gas decreases proportionally, indicative of a perfect negative linear correlation.

Understanding these relationships is crucial, particularly when applying techniques such as linear regression to predict outcomes or to evaluate the strength of the connection between variables. By calculating a correlation coefficient, we can quantify the degree of correlation, where +1 represents a perfect positive linear correlation, -1 represents a perfect negative linear correlation, and 0 indicates no correlation.

Answer 2

answer below

Step-by-step explanation:

1. price per gallon of gasoline and total cost of gasoline

2. distance from a door and height of a wheelchair ramp

perfect positive linear relationship:

this is a relation that exists between two variables. The pearson correlation is used to check this relationship and if the relationship is 1.0 then it is established that a positive linear relationship exists

negative linear relationship

this is a relationship between variables where the pearson correlation is less than 0. if the value is -1.0 then a negative linear relatioship exists.

price per gallon of gasoline and total cost of gasoline move in the same direction so it is positive.

distance from a door and height of a wheelchair ramp are negative because they do not move in the same direction.