The following regression is fitted using variables identified that could be related to tuition charges ($) of a University.
TUITION = α + β ACCEPT + γ MSAT + λ VSAT
Where ACCEPT = the percentage of applicants that was accepted by the university, MSAT = Median Math SAT score for the freshman class and VSAT = Median English SAT score for the freshman class.
The data was processed using MNITAB and the following is an extract of the output obtained:
The regression equation is
TUITION = (deleted)
Predictor Coef StDev T P
Constant -26780 6115 -4.38 0.000
ACCEPT 116.00 37.17* 0.003
MSAT -4.21 14.12 -0.30 0.767
VSAT 70.85 15.77 4.490.000
S = 2685 R-Sq = 69.6% R-Sq(adj) = 67.7%
Analysis of Variance
Source DF SS MS F P
Regression 3 808139371 269379790 37.37 0.000
Residual Error 49 353193051 7208021
Total 52 1161332421
(i) What is the sample size used in this investigation?
(ii) Conduct a hypothesis test, at the 10% level of significance, to determine whether the regression coefficient “MSAT” is significant.
(iii) Isβsignificantly different from 120?