Question

The table below summarizes nested multiple regression models used to predict a person’s quality of life score.

	Model 1		Model 2		Model 3
	est.	sig.	est.	sig.	est.	sig.
intercept	16.68	<.001	9.16	<.001	7.57	<.001
size of social network	0.59	0.027	0.44	0.076	0.43	0.059
college degree	—		3.73	0.014	3.87	0.030
time (yrs) at current job	—		—		0.91	0.046
# of siblings	—		—		–0.68	0.146
R2R2	3.65%		8.01%		9.60%
ΔR2ΔR2	3.65%		4.36%		1.59%
FF (for ΔR2ΔR2)	5.00(1,132)	0.027	6.20(1,131)	0.014	1.13(2,129)	0.325

Using the model information (parameter estimates and comparative model fit), provide a prediction for the quality of life score for a person with a social network of size 8, a college degree, 4 years at current job, and 3 siblings.
     QOL = ˆy=y^=
Report answer accurate to 2 decimal places.

Be prepared to briefly justify your model choice.

Answer 1

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Answer:

To predict the value of person's quality of life score we will use model 2 because of following reasons:

i) although 4 parameters are taken into consideration in model 3 but it does not explain the quality of life score very much that is the even though it is having 4 independent variables the value of R^2 is just 0.096.

ii) The value of F(for delta R^2) in case of model 3 is 1.13 and the p -value is 0.325 which is quite high and hence not significant that is adding an independent variable does not increase the R^2 value significantly.

iii) in case of model 2 the value of F(for delta R^2) is 6.20 and the p-value is 0.014 which is quite low which implies adding a regressor to model helps increase R^2 value significantly.

The percentage of variation explained by model 1 is only 3.65 that is very low compared to model 2, so if enough of the variation is not explained it can't predict accurate observations further.

The predicted value of quality of life score using model 2 is

yhat = 9.16 + 0.44*8 + 3.73*1= 16.41