Functions with a single independent variable are called univariate functions. There is a one to one correspondence. Functions with more than one independent variable are called multivariate functions. The independent variable is often designated by x. The dependent variable is often designated by y. It means that mathematically y depends on x. If we know the value of x, then we can find the value of y. In pronunciation we say " y is f of x. In other words the parenthesis does not mean that f is multiplied by x.
It is not necessary to use the letter f. We may look at functions algebraically or graphically. If we use algebra we look at equations. If we use geometry we use graphs. This is an example of a function that says the price of pizza depends on the prices of tomato sauce, cheese, and pizza dough.
There is one dependent variable, the price of pizza and there are three independent variables, the prices of tomato sauce, cheese, and pizza dough. This is another example of a function. It says that the quantity of pizza demanded depends on the price of pizza and the number of potential pizza eaters.
There is one dependent variable, the quantity of pizza demanded, and there are two independent variables, the price of pizza and the number of potential pizza eaters.
This is an example of a function that says the amount spent on consumption depends on income. This is a very general form of the consumption function.
In order to use it economists must put it into a more precise mathematical form. For example. This is a function which says that consumption is 25 regardless of the level of income and that for every extra dollar of income 75 cents are spent on consumption.
This is a function that says that, y, a dependent variable, depends on x, an independent variable. The independent variable, x, can have different values. Other factors such as what they eat, how much they go to school, how much television they watch aren't going to change a person's age. In fact, when you are looking for some kind of relationship between variables you are trying to see if the independent variable causes some kind of change in the other variables, or dependent variables.
Answer: Just like an independent variable, a dependent variable is exactly what it sounds like. It is something that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.
Usually when you are looking for a relationship between two things you are trying to find out what makes the dependent variable change the way it does. Many people have trouble remembering which is the independent variable and which is the dependent variable. An easy way to remember is to insert the names of the two variables you are using in this sentence in they way that makes the most sense.
To test whether the medication is effective, you divide your patients into two groups. One group takes the medication, while the other group takes a sugar pill placebo. The independent variable is usually applied at different levels to see how the outcome differs. You can apply just two levels e. You can also apply multiple levels e. Instead, they must find already-existing examples of the independent variable, and investigate how changes in this variable affect the dependent variable.
Instead, you look at a state that raised its minimum wage last year, and compare it to a neighboring state that did not. By comparing the difference in outcomes between the two states and accounting for other factors , you can investigate whether the change in minimum wage had an effect on employment rates.
These are known as confounding variables. In types of research where the exact relationship between variables is less certain, you might use different terms for independent and dependent variables.
Sometimes, the variable you think is the cause might not be fully independent — it might be influenced by other variables. In this case, one of these terms is more appropriate:.
See an example. Researchers often use charts or graphs to visualize the results of their studies. For instance, how might a graph look from our example study on the impact of a new medication on blood pressure?
Frequently asked questions What are independent and dependent variables? You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect. In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:.
Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design. Determining cause and effect is one of the most important parts of scientific research.
You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time.
It must be either the cause or the effect, not both!
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