The difference between dependet and independent variables

With more then a million teachers set to retire we are seeing a record number of turnovers in the teaching profession. In a time where student enrollments across America are increasing at a rapid place experts predict that we will need more then two million teachers over the next decade. Clearly define the dependent and independent variables for the shortage of teachers in the United States. The dependent variable is the variable whose value is the result or is a function of the control or independent variables.

Solution Preview

This problem discusses the number of teachers required as a function of time.

Independent variable:
A manipulated variable in an experiment or study whose presence or degree determines the change in the dependent variable.

No one can really "manipulate" time, however one can choose the time interval in which measurements of the dependent variable will be taken. Thus the time variable is the independent variable in this situation.

Dependent variable: ...

Solution Summary

The solution demonstrates what is the difference between independent and dependent variable and how to distinguish between them.

In a typical algebraic expression, there are two variables: an independent variable and a dependent variable. Theindependent variable is the number or the value that can change. The dependent variable's value depends on the value of theindependent variable.
For example, in the following formula, X=Y*5
Y is theindependent

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1. A coin is tossed 3 times. Discrete random variable X is equal to the number of times Heads comes up. Discrete random variable Y has the value 1 if the first toss comes up heads and 0 otherwise.
(a) Find Pr[(X=1)n(y=1)]
Are X and Y independent random variables?

Consider the set of dependent andindependentvariables that can be found in the attached Excel file Prob 151.xlsx.
a) construct a regression model using both independentvariables
b) test the significance of each independent variable using alpha = 0.05
c) interpret the p-value for each independent variable
Data set
y x

Read chapter 7 to answer question below:
What is thedifferencebetween individual differences variablesand manipulated independentvariables? What impact does this difference have on causal inferences? Please give and example of each.
Responses should be at least 250 words.

In a regression analysis with multiple independentvariables, multicollinearity can be caused by:
A- A strong nonlinear relationship betweenthe dependent variable and one or more independentvariables.
B-A strong heteroskedastic relationship betweenthe dependent variable and one or more independent variable.