Question

In: Statistics and Probability

A student used multiple regression analysis to study how family spending (y) is influenced by income...

Anova
	df	ss
regression	3	45.9634
residual	11	2.6218
Total

	coefficient	Standard error
intercept	0.0136
x1	0.7992	0.074
x2	0.2280	0.190
x3	-0.5796	0.920

Calculate the estimated regression equation for the relationship between the variables,coefficient of determination. What can you say about the strength of this relationship,Carry out a test to determine whether y is significantly related to the independent variables and Carry out a test to see if x3 and y are significantly related.

Use a 5% level of significance.

Solutions

Expert Solution

Sol:

Estimated regression eq uation is

y^=0.0136+0.7992*x1+0.2280*x2-0.5796*x3

,coefficient of determination=R sq=1-ss reg/ ss total

=1-(45.9634/48.5852)

= 0.9460371

=0.9460371*100

=94.60% avriation in y is expolained by model

R sq=0.9560

r=sqrt(0.9560)

= 0.9777525

There exists a strong positive relationship between y and indpeendent variable

Carry out a test to determine whether y is significantly related to the independent variables

Ho:beta1=beta2=beta3=0

Ha:atleast one of the betai is not =0

alpha=0.05

F=MS regressssion/MS residual

MS regresssion=SS regression/df

=45.9634/3

=15.32113

MS residual=Ss residual/df residual

=2.6218/11

=0.2383455

F=15.32113/0.2383455

F= 64.28118

p value in excel=

=F.DIST.RT( 64.28118,3,11)

=2.93051E-07

p value=0.000000293

p<0.05

Reject Ho

Accept Ha

Cocnlsuion:

There is suffcient statistical evidence at 5% level of significance to conclude

there is arelationship between y and independent variables that y is significantly related to the independent variables (x1,x2,x3)

Carry out a test to see if x3 and y are significantly related.

Ho:beta3=0

Ha:beta3 not =0

alpha=0.05

t stat=coeffcient/standard error

=-0.5796/0.920

=-0.63

df=n-k-1=15-3-1=11

=T.DIST.2T(0.63,11)

=0.54155995

p value>0.05

Fail to reject Ho

Accept Ho

There is no suffcient statistical evidence at 5% level of significance to conclude that y and x3 are related

x3 is not a significant variable in predicting y

-0.5796

0.920

orchestra answered 1 year ago

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