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 txt from the table in the image is provided below:

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

(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 : 1444

Let us solve this step by step manually. We are given data for Age (X) and Systolic Blood Pressure (Y) for Non-Smokers and Smokers. We are asked to fit a multiple regression model with Smoking Status as a categorical variable and Age as a continuous variable. --- ### Step 1: Encode Smoking Status Let us define a dummy variable: [ S = \begin{cases} 0 & \text{Non-Smoker} \ 1 & \text{Smoker} \end{cases} ] We have 8 Non-Smokers and 7 Smokers. --- ### Step 2: Set up the multiple regression model The model is: [ Y = \beta_0 + \beta_1 X + \beta_2 S + \varepsilon ] Where: * (Y) = Systolic BP * (X) = Age * (S) = Smoking Status (0 = Non-Smoker, 1 = Smoker) We need to calculate (\beta_0, \beta_1, \beta_2) using the least squares method. --- ### Step 3: Calculate necessary sums Combine all data: | Patient | X | Y | S | | ------- | -- | --- | - | | 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 | | 1 | 35 | 128 | 1 | | 2 | 42 | 135 | 1 | | 3 | 48 | 142 | 1 | | 4 | 53 | 148 | 1 | | 5 | 58 | 155 | 1 | | 6 | 62 | 158 | 1 | | 7 | 68 | 165 | 1 | We need: (n, \sum X, \sum Y, \sum S, \sum XY, \sum XS, \sum YS, \sum X^2, \sum S^2) #### Non-Smokers (S=0) * n₀ = 8 * ΣX₀ = 40+45+50+55+60+65+70+75 = 460 * ΣY₀ = 120+124+130+132+138+142+145+150 = 1081 ΣX₀² = 40²+45²+50²+55²+60²+65²+70²+75² 40²=1600 45²=2025 50²=2500 55²=3025 60²=3600 65²=4225 70²=4900 75²=5625 ΣX₀² = 1600+2025+2500+3025+3600+4225+4900+5625 = 27,500 ΣXY₀ = 40*120 + 45*124 + 50*130 + 55*132 + 60*138 + 65*142 + 70*145 + 75*150 Compute step by step: * 40*120=4800 * 45*124=5580 → 4800+5580=10380 * 50*130=6500 → 10380+6500=16880 * 55*132=7260 → 16880+7260=24140 * 60*138=8280 → 24140+8280=32420 * 65*142=9230 → 32420+9230=41650 * 70*145=10150 → 41650+10150=51800 * 75*150=11250 → 51800+11250=63050 ΣXY₀ = 63,050 --- #### Smokers (S=1) * n₁ = 7 * ΣX₁ = 35+42+48+53+58+62+68 = 366 * ΣY₁ = 128+135+142+148+155+158+165 = 1031 ΣX₁² = 35²+42²+48²+53²+58²+62²+68² * 35²=1225 * 42²=1764 → 1225+1764=2989 * 48²=2304 → 2989+2304=5293 * 53²=2809 → 5293+2809=8102 * 58²=3364 → 8102+3364=11466 * 62²=3844 → 11466+3844=15310 * 68²=4624 → 15310+4624=19934 ΣX₁² = 19,934 ΣXY₁

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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

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

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

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

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