3+3 \\\\\\= 6 pt) A survey was conducted to determine a Syracuse University graduate student's overall satisfaction with her/his program of study. The following regression model was used to analyze the data:

Y =₀+ ₁X₁+ ₂X₂+ ₃X₃+ ₄X₄+

where: Y = satisfaction score;

X₁= age (in years);

X₂= number of years of work experience before joining the program;

X₃= the respondent's rating of the quality of teaching at Syracuse University;

X₄= the respondent's rating of the placement services at Syracuse University;

Epsilon () is the random error defined as usual.

You collected data from a simple random sample of 45 respondents and estimated several regression models. The results are as follows:

Model

Dependent Variable

Independent Variable(s)

R²

1

Y

X₁, X₂, X₃, X₄

0.50

2

Y

X₁

0.10

3

Y

X₂

0.25

4

Y

X₃

0.20

5

Y

X₄

0.18

6

Y

X₁, X₂

0.30

7

Y

X₃, X₄

0.35

8

Y

X₁, X₂, X₃

0.44

9

Y

X₁, X₂, X₄

0.46

10

Y

X₁, X₃, X₄

0.40

11

Y

X₂, X₃, X₄

0.48

2.(a) At a 99% level of confidence, test the null hypothesis that ₃= ₄= 0.