
| Title Name | IGNOU MST 17 SOLVED ASSIGNMENT |
|---|---|
| Type | Soft Copy (E-Assignment) .pdf |
| University | IGNOU |
| Degree | MASTER DEGREE PROGRAMMES |
| Course Code | MSCAST |
| Course Name | M.Sc. (Applied Statistics) |
| Subject Code | MST 17 |
| Subject Name | Applied Regression Analysis |
| Year | 2025 |
| Session | |
| Language | English Medium |
| Assignment Code | MST-017/Assignmentt-1//2025 |
| Product Description | Assignment of MSCAST (M.Sc. (Applied Statistics)) 2025. Latest MST 017 2025 Solved Assignment Solutions |
| Last Date of IGNOU Assignment Submission | Last Date of Submission of IGNOU MST-017 (MSCAST) 2025 Assignment is for January 2025 Session: 30th September, 2025 (for December 2025 Term End Exam).Semester WiseJanuary 2025 Session: 30th March, 2025 (for June 2025 Term End Exam).July 2025 Session: 30th September, 2025 (for December 2025 Term End Exam). |
Ques 1.
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)].
Ques 2.
Write a short note on the problem of multicollinearity and autocorrelation.
Ques 3.
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.
Ques 4.
Explain the assumptions underlying the multiple linear regression model.
Ques 5.
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.
Ques 6.
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?
Ques 7.
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.
Ques 8.
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)].
Ques 9.
Write a short note on the problem of multicollinearity and autocorrelation.
Ques 10.
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.
Ques 11.
Explain the assumptions underlying the multiple linear regression model.
Ques 12.
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.
Ques 13.
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?
Ques 14.
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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| Course Name | M.Sc. (Applied Statistics) |
| Course Code | MSCAST |
| Programm | MASTER DEGREE PROGRAMMES Courses |
| Language | English |
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