SOLUTION: Major help needed in figuring this one out? Respectfully thank you for your help! What is the difference between an independent and a dependent variable? Can independent and

Question 63314This question is from textbook
: Major help needed in figuring this one out? Respectfully thank you for your help!

What is the difference between an independent and a dependent variable? Can independent and dependent variables be interchangeable? Why or why not? Provide an example of this use.

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
2) compute, for batch weight, (a) the sample standard deviation and (b) the standard error of the estimate. Does a comparison of these two values indicate that the regression line would be useful in predicting batch weight? Why or why not?

This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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.
---------------

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)
----------------
2) compute, for batch weight:
(a) the sample standard deviation = s = 6.6207
---------

(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?
-------------
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.
-----------
Cheers,
Stan H.

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