Green Mountain College is a 5,000 student state-supported, four-year institution located in the mid-South. Physical facilities can accommodate another 1,000 students, and the college administration is attempting to estimate the added yearly cost of educating the additional students. The Business Manager of Green Mountain College has asked you to evaluate two linear regressions given below, and recommend the better one to her.



Where: SC = Student cost
CH = Cost per credit hour
IS = Incremental cost per student

Required:
a. Defend your choice of cost function (regression 1 or regression 2) for predicting added student educational costs per year.

Y = a + bx + e

Y = the amount of the dependent variable
A = a fixed quantity
X = the value for the independent variable
B = the unit variable cost
E = the estimation error

MY WORK BELOW:
REGRESSION 1 REGRESSION 2
R-squared = .594 R-squared = .707
t-value = t-value =
standard error = 117 standard error = 133
Y = a + bx + e Y = a + bx + e
Y = a + .594 x + 117 Y = a + .707 x + 133

Not sure how to get t-value or the rest of the formula.

b. What information value does the standard error of estimate (SE) have in this situation?
For situation 1, since the regression estimate is 4,303 and the SE is 117, there is reasonable confidence that the unknown actual value lies in the range 4303 +/- 117, between 4420 and 4186.
For situation 2, since the regression estimate is 3,800 and the SE is 133, there is reasonable confidence that the unknown actual value lies in the range 3,800 +/- 133, between 3933 and 3667.

Does my work look right?

gogosean

Here is one they don't tell you a lot. The Y intercept, which is A, is sometimes considered Fixed Cost. The R squared evaluates % variance that the IV accounts for the DV, so model 2 is a better fit. I would also include the interpretation of the (coefficients/beta weights). Also, you have t values for all predictors, what is <.10 and what is <.05 and why does that matter?
If you only have one IV, that is okay, but numerous IVs will artificially inflate the R2.
Need more? I am kind of tired so I will touch base tomorrow.

PS You have constraints!!!! Don't forget to talk about them, having a limit of 1k additional students is different than unlimited students.

femaleinjax

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Can you explain in more detail or provide me a website that shows detail steps?

Thanks