Explanatory / Response Variables

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Presentation transcript:

Explanatory / Response Variables Scatterplots Explanatory / Response Variables

Scatterplots T. Serino Objective: Students will be able to identify explanatory/response variables and create scatterplots.

Scatterplots T. Serino Scatterplots: Plotting a set of ordered pairs (x, y) on the xy-axes. dependent y x In algebra, we referred to the x-variable as the independent variable and the y-variable as the dependent variable. Depends on independent It can help to remember this by using the statement: “y depends on x” (as shown).

Scatterplots T. Serino Scatterplots: Plotting a set of ordered pairs (x, y) on the xy-axes. response y In statistics, we refer to the x as the explanatory (or predictor) variable and the y as the response variable. (x, y) (independent, dependent) (explanatory, response) x explanatory (predictor) “y responds to x” “x explains (or predicts) y”

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Ask yourself some guiding questions: Does the amount of free time you have depend on the number of classes taken? or Do the number of classes taken depend on the amount of free time you have?

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Similarly: Is the amount of free time you have a response to the number of classes taken? or Is the number of classes taken a response to how much free time you have?

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Another way to look at it is: Does the amount of free time you have explain the number of classes taken? or Does the number of classes taken explain the amount of free time you have?

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Here are the answers to the guiding questions: Does the amount of free time you have depend on the number of classes taken? or Do the number of classes taken depend on the amount of free time you have? Free time depends on classes taken Dependent Independent Response (y) Eplanatory (x)

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Also: Is the amount of free time you have a response to the number of classes taken? or Is the number of classes taken a response to how much free time you have? Free time is a response to classes taken Response (y) Eplanatory (x)

Scatterplots T. Serino Ex) Determine the explanatory (x) and response (y) variables. Amount of free time vs. Number of classes taken Finally: Does the amount of free time you have explain the number of classes taken? or Does the number of classes taken explain the amount of free time you have? Number of classes taken explains your amount of free time Eplanatory (x) Response (y)

Scatterplots T. Serino Any of these questions can be used to figure out which variable is the explanatory and which is the response. Use the one that works for you! Does the amount of free time you have depend on the number of classes taken? or Do the number of classes taken depend on the amount of free time you have? Is the amount of free time you have a response to the number of classes taken? or Is the number of classes taken a response to how much free time you have? Does the amount of free time you have explain the number of classes taken? or Does the number of classes taken explain the amount of free time you have?

Scatterplots T. Serino Example: Identify which is the explanatory and which is the response variable. Response Amount of home energy used vs. Average Daily Temperature Explanatory Does the amount of home energy used depend on the temperature? or Does the temperature depend on how much home energy is used? Does the amount of home energy used explain the temperature? or Does the temperature explain how much home energy is used? Is the amount of home energy used a response to temperature? or Is the temperature a response to how much home energy is used?

Scatterplots T. Serino Ave. Temp. (Deg F) Energy Used (kWh) 60 22 51 40 47 38 42 43 37 50 57 24 52 29 Draw a scatter plot using the following data. Be sure to put the explanatory variable on the x-axis and the response variable on the y-axis.

Number of cars on the road Scatterplots T. Serino Try this: Identify which is the explanatory and which is the response variable. Air Pollution Levels vs. Number of cars on the road Show work by writing the pair of guiding questions you used and identifying the correct guiding question.

Scatterplots T. Serino Cars on Road (Thous) Polution (NO2) 146 70 149 82 152 100 158 140 163 170 168 173 Draw a scatter plot using the following data. Be sure to put the explanatory variable on the x-axis and the response variable on the y-axis.

athematical M D ecision aking