Data were collected from approximately 200 different colleges and universities i
ID: 3259837 • 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
enrollment = b0 + b1*Tution + b2 * Library + b3 * Salary_Prof + b4*SAT_score + b5*Sports + b6* Faculty
any coefficient is regression is interpreted as when other variable remains constant ,by change in 1 unit of independent variable . , there will be change of beta coefficent in dependent variable
here b0 = 13409 when everything else is 0 , then enrollment will be 13409
b1 = -3.457 , if tution is increased by 1 unit , enrollemnt will decrease by 3.457 unit
similarly other
b5 = 4983.843 , if means if it has division 1 program , then there will be 4983.843 more enrollement on average than that in without sports program,
now t-critical for 0.05 significance level is nearly 2 or -2
hence when t-score is more than 2 or less than -2 , the independent variable is significant
here every variable is significant except Library as -2 < -0.628 <2
R^2 = 0.7110
it means that this model explains 71.1 % of total variationa
F = 61.10 which is very high , it means , the given model is significant at 0.05 significance level.
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