Question

1. For the following multiple regression which was conducted to attempt to predict the variable based on the independent variables shown, answer the following questions.

Regression Statistics
Multiple R	0.890579188
R Square	0.793131289
Adjusted R Square	0.7379663
Standard Error	30.28395534
Observations	20
ANOVA
	df	SS	MS	F
Regression	4	52743.23074	13185.81	14.37743932
Residual	15	13756.76926	917.1179509
Total	19	66500
	Coefficients	Standard Error	t Stat	P-value
Intercept	73.33291	62.25276	1.17799	0.25715
X1	-0.13882	0.05353	-2.59326	0.02037
X2	3.73984	0.95568	3.91328	0.00138
X3	0.37644	0.16876	2.23061	0.04140
X4	17.70752	15.57847	1.13667	0.27351

1. Write down the fitted multiple regression equation     

2. Interpret any two β’s

3. Test the Individual significance of the regression hypothesis at the 5% level of significance.

4. Interpret R Square.

Answer 1

Y = 73.33291 -0.13882*x1 + 3.73984*x2 + 0.37644*x3 + 17.70752*x4

................

b)

β1 = -0.13882

if x1 is increased by 1 unit , then Y will decrease by 0.13882 (keeping all other thngs constant)

β2 =3.73984

if x2 is increased by 1 unit , then Y will increase by3.73984 (keeping all other thngs constant)

..............

c)

df		F-stat	p-value
4		14.38	0.0001
15
7

p value < 0.05 , signifcant

modal is significant

..............

R square =   0.7931

so, 79.31 % of data can be explained by independent varaibles of Y

...................

THANKS

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