The following regression is fitted using variables identified that could be rela

Question

The following regression is fitted using variables identified that could be related to student requested loan amount , LOAN-AMT($) for returning students of a certain University.

LOAN-AMT = + ACCEPT + PREV + OUTS

Where ACCEPT = the percentage of applicants that was accepted by the university, PREV = previous loan amount and OUTS =outstanding loan amount

The data was processed using MNITAB and the following is an extract of the output obtained:

The regression equation is LOAN-AMT = -26780 + 116.00ACCEPT – 4.21PREV + 70.85OUTS

S = 2685 R-Sq = 69.6% R-Sq(adj) = 67.7%

Analysis of Variance

(a) What is the sample size used in this investigation?

(b) Fill in the blanks identified by ‘*’ and ‘**’.

(c) Is significant, at the 5% level of significance?

(d) Is significantly different from 120?

(e) If a F-Test is to be conducted, state the appropriate null and alternative hypotheses for this test.

Predictor Coef StDev T P Constant -26780 6115 * 0.000 ACCEPT 116.00 37.17 3.14 0.003 PREV -4.21 14.12 -0.30 ** OUTS 70.85 15.77 4.49 0.000

Explanation / Answer

a. Total degress of freedom = n-1 for n observations = 52 here

So, n = 53 observations

b. * : t = -26780/6115 = -4.38

** p value = 2(P(t<-0.03)) = 2(0.3827) = 0.7654

c. Beta is significant at 5% as p value = 0.003 < 0.05

d. Coefficient for gamma = -4.21 and std error = 14.12. So, CI is -4.21 - 14.12*1.96, -4.21 + 14.12*1.96 .

So, this is beyond 120. Hence significantly different from 120

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