Data were collected from approximately 200 different colleges and universities i
ID: 3245343 • Letter: D
Question
Data were collected from approximately 200 different colleges and universities in the United States for the year 2012. The goal was to predict enrollment. The study revealed the following:
Coefficient T Score
Intercept 13409.000 2.309
Tuition -3.457 -3.288
Library (number of books in thousand) -0.427 -0.628
Salary (average salary of Full Professors at the school) 0.731 2.711
SAT (average score for entering freshmen) -17.043 -2.431
Sports (0,1 dummy variable, 1 if school has division 1 program) 4983.843 4.137
Faculty (Number of full time faculty on staff) 7.199 9.019
R2 = 0.7110
F = 61.10
Fully Evaluate and Interpret these empirical results on the basis of all available statistics (use a 0.05 significance level).
Explanation / Answer
The equation for predicted model is
enrollment ^ = 13409 -3.457*Tuition -0.427 * Library+0.731*Salary -17.043*SAT +4983.843*Sports +7.199 *Faculty
t-critical for 0.05 significance level is 1.96
if t > 1.96 or t< -1.96 ,we reject the null hypothesis ,
so all independent variables are significant except Library {-1.96 < -0.628 < 1.96 }
R^2 = 0.7110 ,which is good fit
F = 61.10 as
critical F
n1 = k = 6 indenpendent variable
n2 = n-k-1 = 200-6-1 = 193
F( 6,193) = 2.15
and 61.1 > 2.15
,hence the model is significant at 0.05 significance level).
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