Independent and dependent variables
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Independent and Dependent Variables. Correlation. Continuous and Discrete Data. In an Algebraic situation, equation , table, or graph, the variables (usually x and y) can be classified as either __________ or _________. independent. dependent. Independent Variable. x-axis.

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Independent and Dependent Variables

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Independent and dependent variables

Independentand Dependent Variables

Correlation

Continuous and Discrete Data


Independent and dependent variables

In an Algebraic situation, equation, table, or graph, the variables (usually x and y) can be classified as either __________ or _________.

independent

dependent


Independent variable

Independent Variable

x-axis

The independent variable is always located on the _________ of a graph.

The independent variable is the ________________.

It is usually the ________ in a table or equation.

The independent variable STANDS ALONE (___________).

The independent variable is what happens _______.

Input (domain)

“x”

Does not depend

FIRST


Independent and dependent variables

The variable in a function whose value is subject to choice is the independent variable. The independent variable affects the value of the dependent variable.


Dependent variable

Dependent Variable

The dependent variable is always located on the _________ of a graph.

The dependent variable is the ______________.

It is usually the _______ in a table or equation.

The dependent variable DEPENDS on the

________________.

The dependent variable is what happens _______.

y-axis

Output (Range)

“y”

independent variable

2nd


Independent and dependent variables

The variable in a function whose value is determined by the independent variable.


Let s practice

Let’s Practice!

  • A student’s grade depends on how much she studies.

    Independent variable:__________

    Dependent variable:___________

    2. The height of a plant and the amount you water it.

    Independent variable: ___________

    Dependent variable: _____________

Time studying

grade

Amount watered

height


Independent and dependent variables

3. The amount of money you make and the number of hours you work.

Independent variable: _____________

Dependent variable:_____________

4. The number of sodas you buy and the total money spent.

Independent variable:______________

Dependent variable:_______________

5. The number of houses you can paint depends on how much time you have.

Independent variable:______________

Dependent variable:_______________

Hours worked

Amount of money

Number of sodas

Total money

Amount of time

Number of houses


Continuous data

Continuous Data

Data that is continuous is data that _________ happens. You can usually tell that your data is continuous if you are _________ something (i.e. time, distance, length, height, etc.). If your data is continuous, then you will _________ the points on your graph.

continuously

measuring

connect


Discrete data

Discrete Data

You can tell that your data is discrete if you are ________________________ (i.e. number of people, cars, or stories of a building). If your data is discrete, then you will _____________ the points on your graph.

counting or measuring in whole numbers

NOT connect


Independent and dependent variables

  • Graphs of each situation


Let s practice1

Let’s Practice

Look at the situations given in examples 1-5. Decide if the situation would best be classified as either discrete or continuous data.

1. A student’s grade depends on how much she studies.

2. The height of a plant and the amount you water it.

3. The amount of money you make and the number of hours you work.

4. The number of sodas you buy and the total money spent.

5. The number of houses you can paint depends on how much time you have.

continuous

continuous

discrete

discrete

continuous


Example

Example

Kadence collected data on the number of push-ups she could do in 2 minutes. The table below shows her data.

Time (seconds)

  • What is the independent variable?

  • Is the data continuous or discrete?

Discrete – counting push-ups


Independent and dependent variables

Correlation

  • It is the relationship that exists between two variables (Independent and dependent).


Independent and dependent variables

y

x

Positive Correlation

  • As one variable increases, so does the other.


Example of positive correlation

Example of positive correlation…

The longer you exercise, the more calories you burn.

*As exercise increases, calories burned increases

Can you think of one?


Negative correlation

y

x

Negative Correlation:

  • As one variable increases, the other decreases.


Example of negative correlation

Example of negative correlation…

The longer the air conditioner is turned on, the colder the temperature.

*As time increases, the temperature decreases

Can you think of one?


No correlation

y

x

No Correlation:

  • As one variable increases, you cannot tell what the other is doing.


Independent and dependent variables

Example of no correlation…

The number of students in the classroom and the average height.

*As the number of students increases, you cannot tell what the average height will do.

Can you think of one?


Everything

Everything…

The amount of time you spend in an airplane and the distance between your departure and your destination.

1. What are the independent and dependent variables?

Independent: Distance Dependent: Time

2. Would this situation represent a discrete or continuous situation?

Continuous

3. What type of correlation is represented in this situation?

Negative correlation


Independent and dependent variables

Everything again…

The number of times you dip a wick into hot wax and the diameter of a handmade candle

1. What are the independent and dependent variables?

Independent: The number of dips Dependent: diameter of candle

2. Would this situation represent a discrete or continuous situation?

Discrete

3. What type of correlation is represented in this situation?

Positive correlation


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