Question 63314
What is the difference between an independent and a dependent variable?
An independent variable is given an arbitrary value; the dependent 
variable is then calculated based on the rule and the independent 
variable value.

 Can independent and dependent variables be interchangeable? Why or why not? 
Yes.  It is a matter of point of view.
Provide an example of this use.
If y=3x+6 the x is considered to be the independent variable.
The same equation states x=(y-6)/3; the y could be considered to
be the independent variable.
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      For example, cost accountant Linda Thomas provided the following sampling data for observations obtained during an investigation of the relationship between the volume of an ingredient X and the weight of a production batch Y. 

 

Volume X. Weight Y
 
10          61
 24          110
 13          75
 7           47
 9           78
 25          102
 6            38
 10           42
 16           75
 15           91
 
Note:  When submitting this question the columns all come together.  There are two columns going down but they don't seem to line up when submitting the question.
 

1)       determine the estimated regression equation
y=3.32x+26.99 (Gotten using TI-83 Linear Regression function)
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2)       compute, for batch weight:
(a) the sample standard deviation = s =  6.6207
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(b) the standard error of the estimate

SE=s/sqrt(10)= 2.09365

. Does a comparison of these two values indicate that the  regression line would be useful in predicting batch weight? Why or why not?
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The smaller the standard error the better the predictability of the 
regression line.  I don't know what criteria you are using for "small"
so I'll let you decide wether 2.09365 is small enough.
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Cheers,
Stan H.