Question

The data presented in worksheet 4 is the results of a 4-year study conducted to assess how age, weight, and gender influence the risk of diabetes. Risk is interpreted as the probability (times 100) that the patient will have diabetes over the next 4-year period.

a) What predictive model you suggest to relate risk of diabetes to the person’s age, weight and the gender. Why? b)Develop an estimated multiple regression model that relates risk of diabetes to the person’s age, weight, gender and life style. Present the regression formula as a mathematical equation. Interpret the coefficients of the regression and comment on the strength of the regression.

c) What is the risk percentage of diabetes over the next 4 years for a 52-year-old woman living in a small town with 80 kg weight?

Age	Weight (Kg)	Gender	Life style	Risk (%)
56	80	Female	Small town	38
27	79	Male	Big city	23
80	85	Female	Country	67
91	91	Female	Small town	71
59	67	Male	Big city	45
74	84	Female	Country	54
56	81	Female	Small town	48
73	68	Male	Small town	49
83	82	Female	Big city	65
81	69	Male	Big city	59
74	71	Male	Big city	56
73	80	Female	Small town	59
70	77	Male	Country	46
80	90	Female	Big city	64
63	59	Male	Country	39
85	102	Female	Big city	73
69	87	Male	Small town	63
83	98	Male	Big city	87
65	85	Female	Country	52
62	95	Male	Big city	61
79	69	Male	Big city	59
57	77	Female	Small town	46
81	51	Male	Big city	64
72	60	Male	Country	64

Answer 1

Note : since no methodology was mentioned in the question, Excel was used.

Please consider this while giving your feedback.

Answer :

a)

Predictive Model will be Multiple Regression model (MR)

Because, the dependent variable ( Risk) is an Interval data. MR  examines how multiple independent variables are related to one dependent variable.

b)

Estimated Regression Model:

Risk_percentage = -33.2447+0.8042(Age)+0.3997(Weight)+4.7667(Gender)-0.6328(Life_style) .................(1)

( Refer Excel output below )

Note : Coding as below ;

Male=1 and Female=0

Big city =1, Country=2, small town=3

##### Excel Output

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.91225837
R Square	0.832215333
Adjusted R Square	0.796892245
Standard Error	6.034253584
Observations	24
ANOVA
	df	SS	MS	F	Significance F
Regression	4	3431.501223	857.8753058	23.56009583	3.84443E-07
Residual	19	691.83211	36.41221631
Total	23	4123.333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-33.2447	13.4646	-2.4690	0.0232	-61.4264	-5.0630
Age	0.8042	0.0959	8.3841	0.0000	0.6035	1.0050
Weight_in_Kg	0.3997	0.1166	3.4262	0.0028	0.1555	0.6438
Gender	4.7667	3.1677	1.5048	0.1488	-1.8634	11.3968
Life_style	-0.6328	1.6303	-0.3882	0.7022	-4.0450	2.7793

##########

ii)  Interpret the coefficients of the regression and comment on the strength of the regression.

Age : For every one unit increase in Age , the Risk will increase by 0.8042%

Weight_in_Kg : For every one unit increase in Weight_in_Kg, the Risk will increase by 0.3997%

Gender : For Males , the Risk will increase by 4.7667% as compared to Females

Life_style : For Life_style (1,2,3) , the Risk will decrease by 0.6328%

################

c)

What is the risk percentage of diabetes over the next 4 years for a 52-year-old woman living in a small town with 80 kg weight?

Put these value in the above equation (1), we get;

Risk_percentage = -33.2447+0.8042(Age)+0.3997(Weight)+4.7667(Gender)-0.6328(Life_style)

Risk_percentage = -33.2447+0.8042(56)+0.3997(80)+4.7667(0)-0.6328(3)

Risk_percentage = 41.8681 ( 42% )

##############

#### End of Answers

Note : Since no methodology was mentioned in the question, Excel was used.

Please consider this while giving your feedback.