IGNOU MST 17 2026 - To investigate the effect of Age (in years) and Smoking Status (Group

Question

To investigate the effect of Age (in years) and Smoking Status (Group 1: Non-Smokers, Group 2: Smokers) on Systolic Blood Pressure (in mmHg), the following data were collected:

The text from the table in the image is provided below:

Non-smoker			Smoker
Patient	Age (X)	Systolic Blood Pressure (Y)	Patient	Age (X)	Systolic Blood Pressure (Y)
1	40	120	1	35	128
2	45	124	2	42	135
3	50	130	3	48	142
4	55	132	4	53	148
5	60	138	5	58	155
6	65	142	6	62	158
7	70	145	7	68	165
8	75	150

(i) Fit a multiple regression model.

(ii) Obtain the individual regression models for Non-Smokers and Smokers separately based on the main model.

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

25 Mar 2026

Answer :

Word Count : 777

We are asked to solve a multiple regression problem numerically using the provided data for age, smoking status, and systolic blood pressure. Let's go step by step. --- Step 1: Organize the data for multiple regression We define: * (Y) = Systolic Blood Pressure * (X_1) = Age * (X_2) = Smoking Status (0 = Non-smoker, 1 = Smoker) From the table: | Patient | Age (X1) | SBP (Y) | Smoking (X2) | | ------- | -------- | ------- | ------------ | | 1 | 40 | 120 | 0 | | 2 | 45 | 124 | 0 | | 3 | 50 | 130 | 0 | | 4 | 55 | 132 | 0 | | 5 | 60 | 138 | 0 | | 6 | 65 | 142 | 0 | | 7 | 70 | 145 | 0 | | 8 | 75 | 150 | 0 | | 9 | 35 | 128 | 1 | | 10 | 42 | 135 | 1 | | 11 | 48 | 142 | 1 | | 12 | 53 | 148 | 1 | | 13 | 58 | 155 | 1 | | 14 | 62 | 158 | 1 | | 15 | 68 | 165 | 1 | Total (n = 15). We use the multiple regression model: [ Y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \varepsilon ] --- Step 2: Compute necessary sums Let’s compute the sums manually: Non-smokers (X2 = 0) [ \sum X_1 = 40+45+50+55+60+65+70+75 = 460 ] [ \sum Y = 120+124+130+132+138+142+145+150 = 1081 ] Smokers (X2 = 1) [ \sum X_1 = 35+42+48+53+58+62+68 = 366 ] [ \sum Y = 128+135+142+148+155+158+165 = 1031 ] Overall sums [ \sum X_1 = 460 + 366 = 826 ] [ \sum X_2 = 0*8 + 1*7

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Related Questions

on-smoker			Smoker
Patient	Age (X)	Systolic Blood Pressure (Y)	Patient	Age (X)	Systolic Blood Pressure (Y)
1	40	120	1	35	128
2	45	124	2	42	135
3	50	130	3	48	142
4	55	132	4	53	148
5	60	138	5	58	155
6	65	142	6	62	158
7	70	145	7	68	165
8	75	150

S. No.	Concentration ($x_i$)	Recovered ($y_i$)	Total Subjects ($n_i$)
1	2	10	50
2	4	15	45
3	6	22	40
4	8	35	60
5	10	68	80

Driver	Experience ($X_1$)	Sleep ($X_2$)	Efficiency ($Y$)
1	2	8	75
2	5	7	82
3	10	6	88
4	1	5	60
5	8	8	95
6	4	7	78
7	3	6	72
8	12	7	98
9	7	4	80
10	6	9	90

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