Question

Question C [SD1: 5 Marks]

            A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X₁), age of the individuals (X₂), and the gender of the individual (X₃; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained.

	Coefficients	Standard Error
Intercept	4.0928	1.4400
X1	10.0230	1.6512
X2	0.1020	0.1225
X3	-4.4811	1.4400

ANOVA
		DF	SS	MS	F
Regression			360.59
Residual (Error) Required:			23.91
1-	Interpret the meaning of the coefficient of X3.
2-	Is the coefficient of X3 significant? Use a = 0.05.
3-	Perform an F test and determine whether or not the model is significant.

Answer 1

The regression equation will be

Here n=10, k=3

1. Interpret the meaning of the coefficient of

ans-

The male's income is lower then the female's income

that is, if the gender is male then the income reduces to

2. Is the coefficient of significant? use

ans-

Here total sample size n=10

For t-test degree of freedom will be n-k-1=10-3-1=6

so for 6 degree of freedom and 0.005 level of critical value of t=2.447

so reject null hypothesis if or

Null hypothesis

Alternative hypothesis

coefficient / standard error

Here the the critical value so reject

coefficient of is significant.

3. Perform an F test and determine whether or not the model is significant.

ans-

MS regression=SS regression / DF regression

=360.59/3

=120.1967

MS residual=SS residual / DF resudual

=23.91/6

=3.985

F=MS regression / MS residual

=120.1967/3.985

=15.08

For 0.05 level and 3,6 degree of freedom critical value F=4.757

so null hypothesis will be rejected if

ANOVA
	DF	SS	MS	F
regression	k=3	360.59	120.1967	30.1622
residual	n-k-1=6	23.91	3.985
	9	384.5

Here 30.1622 is greater then the critical value.

Model is significant.