Please provide detailed explanation and solution for the Econometrics question b

Question

Please provide detailed explanation and solution for the Econometrics question below. Use Screenshot, and include all the test formula please.

Please answer every single question and give out explanation.

(Please don't intentionally give wrong answers just to earn the score --because I really want to learn how to do this with comprehension. Thanks!!)

2. Multiple restriction test You have just been hired at the University of California, Berkeley Office of the President to determine student success. You are using GPA for the term and the course final exams for your dependent variables. Your boss just entered the room with your first assignment. She wants to look as the relevant factors associated with term GPA'. She asks you to estimate the following model. Term GPA, = + ,Cumulative GPA, + 2ACT Score, + ,Percent Classes Attended Percent Homework Completed, + ,Freshman, + ,sophomore, + i +

Explanation / Answer

The problem is of multiple regression.

Dependent variable : Term GPA

Independent variables : Cumulative GPA, ACT score, percent classes attended, percent homework completed, freshman and sop honore

First we have to complete both the table then only we can give answers.

Formulae :

MSmodel = SSmodel/dfmodel

MSres = SSres / dfres

F = MSmodel / MSres

P-value we can find in EXCEL.

syntax :

=FDIST(s, deg_freedom1, deg_freedom2)

where x is test statistic

deg_freedom1 = degrees of freedom for model

deg_freedom2 = degrees of freedom for residual

Test statistic (t) = coeff / std error

P-value in EXCEL.

syntax :

=TDIST(x, deg_freedom, tails)

where x is absolute value of test statistic.

deg_freedom = n-1 = 673-1 = 672

tails = 2

R-sq = 1 - SSRes / SSTot

= 1 - 151.233868/353.748658

= 0.5725 = 57.25%

a) Here we have to test,

H0 : B = 0 Vs H1 : B not=0

where B is population slope for independent variable.

Assume alpha = 0.05

Test statistic follows t-distribution.

Decision rule :

If P-value < alpha (0.05) then reject H0 otherwise accept H0.

In the second table we see that cumGPA, ACT, percentclass and percenthomework are significant variables while frosh and soph are insignificant variables.

b) Here we need R square.

R-sq = 57.25%

c) Here we need adjusted R square.

Adj R-sq = 0.5686 = 56.86%

d) Here we have to test the hypothesis that,

H0 : Bj = 0 Vs H1 : Bj not= 0

where Bj is population slope for jth independent variable.

Assume alpha = level of significance = 0.05

Here test statistic follows F-distribution.

Test statistic = 148.8615

P-value = 1.548E-119 = 0.000

P-value <alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the slope is differ than 0.

We get significant result about F test.

source SS df MS F P-value model 202.51479 6 33.752465 148.8615 1.548E-119 residual 151.233868 667 0.226737433 total 353.748658 673

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