IGNOU MSTE 4 2026 - To study the relationship between age (in years) and cholesterol

Question

To study the relationship between age (in years) and cholesterol level (in mg/dL) of two groups of patients, the following data were recorded:

Group 1

Age (years)	46	52	39	65	54	49	76	71
Cholesterol	185	218	182	220	224	193	232	228

Group 2

Age (years)	20	33	78	51	43	44	63
Cholesterol	180	238	275	244	242	268	260

(i) Fit the multiple regression model.

(ii) Obtain the regression models for each group separately.

(iii) Test the significance of the fitted model at 5% level of significance.

19 Jan 2026

Answer :

Word Count : 206

Let (Y) denote cholesterol level (mg/dL) and (X) denote age (years). Define a dummy variable (D) such that (D=0) for Group 1 and (D=1) for Group 2. For all 15 observations, the multiple regression model is taken as [ Y=\beta_0+\beta_1X+\beta_2D+e . ] Using the combined data, the normal equations obtained from (\sum Y,\sum X,\sum D,\sum X^2,\sum XD,\sum XY,\sum DY) give the estimates [ \hat\beta_0=155.3,\qquad \hat\beta_1=1.02,\qquad \hat\beta_2=37.6.

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Related Questions

Participant ID	CHD Time
P1	5
P2	8
P3	2
P4	6+
P5	9
P6	6
P7	10+
P8	4
P9	8
P10	4+

S. No.	`x_i`	`y_i`	`n_i`
1	5	24	60
2	10	18	48
3	15	12	40
4	20	20	80
5	25	26	104

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