IGNOU MST 17 SOLVED ASSIGNMENT

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MST 017 (January 2025 - July 2025) - ENGLISH

MST-017: Applied Regression Analysis

Course Code: MST-017

Assignment Code: MST-017/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

1(a) State whether the following statements are true or false and also give the reason in support of your answer.

(i) We define three indicator variables for an explanatory variable with three categories.

(ii) If the coefficient of determination is 0.833, the number of observations and explanatory variables are 12 and 3, respectively, then the Adjusted R² will be 0.84.

(iii) For a simple regression model fitted on 15 observations, if we have h₁ = 0.37, then it is an indication to trace the leverage point in the regression model.

(iv) In a regression model  is not rejected, then the variable X₁ will remain in the model.

(v) The logit link function is log [-log(1-π)].

(b) Write a short note on the problem of multicollinearity and autocorrelation.

2 Suppose a researcher wants to evaluate the effect of cholesterol on the blood pressure. The following data on serum cholesterol (in mg/dL) and systolic blood pressure (in mm/Hg) were obtained for 15 patients to explore the relationship between cholesterol and blood pressure:

S. No	. Cholesterol (mg/dL)	SBP (mm/Hg)
1	300	150
2	410	270
3	380	210
4	530	310
5	570	350
6	490	310
7	340	210
8	320	150
9	280	110
10	550	320
11	340	220
12	350	170
13	410	260
14	390	230
15	450	270

(i) Fit a linear regression model using the method of least squares.

(ii) Construct the normal probability plot for the regression model fitted on serum cholesterol and systolic blood pressure.

(iii) Test the significance of the fitted regression model.

3(a) Explain the assumptions underlying the multiple linear regression model.

(b) For the data given in Question 2(b), obtain the followings:

(i) Diagonal of the hat matrix. Also, check the leverage points, if any.

(ii) Cook’s Distances. Also, verify the influence points, if any.

4 A company conducted a study on its employees to see the relationship of several variables with an employee’s IQ. For this purpose, fifteen employees were selected, and an IQ test and five different personality tests were given to them. Each employee’s IQ was recorded along with scores on five tests. The data are shown in the following table

Employee	Test 1	Test 1	Test 3	Test 4	Test 5	IQ
1	83	80	78	77	67	99
2	73	85	67	80	63	92
3	81	80	71	81	68	94
4	96	86	82	83	56	99
5	84	73	75	75	68	94
6	72	74	71	67	59	79
7	84	79	84	84	69	97
8	54	86	61	69	53	92
9	86	85	79	78	76	94
10	42	71	60	80	56	86
11	83	72	72	78	74	98
12	63	86	65	85	56	83
13	69	76	64	85	61	98
14	81	84	65	85	64	96

Determine the most appropriate regression model for the employee’s IQ using a stepwise approach at a 5 % level of significance and interpret the results. Does the final regression model satisfy the linearity and normality assumptions?

5. The following data on the diagnosis of coronary heart disease (where 0 indicates absence and 1 indicates presence), serum cholesterol (in mg/dl), and weight (in kg) were obtained for 80 patients to explore the relationship of coronary heart disease with cholesterol and weight:

S. No.	Serum Cholesterol (mg/dl)	Weight (kg)	Number of Patients having CHD	Total Number of Patients
1	420	60	10	20
2	450	68	15	30
3	400	54	4	15
4	510	74	2	10
5	480	62	1	5

(i) Fit a multiple logistic model for the dependence of coronary heart disease on the  average serum cholesterol and weight considering  as the initial values of the parameters (solve only for one Iteration).

(ii) Test the significance of the fitted model using the Hosmer-Lemeshow test at 5% level of significance.

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