HI this is hussain sheriff Msc Operations research and computer applications.
I attached second semester Model Question Paper ....
DATA ANALYTICS
UNIT-1
1.Given the data X1: 10 5 7 19 11 18 X2: 2 3 3 6 7 9 X3: 15 9 3 25 7 13 Fit the Multiple linear regression models in matrix form; specifically calculate the least squares estimates β, the fitted values y, the residuals ε, and the residual sum of squares ε’ε.
2. Define Regression. Scores made by the students in a class in the mid- term and final examination are given here. Develop a regression equation which may be used to predict final examination scores from the mid-term score and also find the estimated final score of a student for mid-term score is 50. STUDENT: 1 2 3 4 5 6 7 8 9 10 MID-TERM: 98 66 100 96 88 45 76 60 74 82 FINAL: 90 74 98 88 80 62 78 74 86 80
3. The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature(X1), the number of days in the month(X2). The past year’s historical data are available and are presented in the following table. Y 240 236 270 274 301 316 300 296 267 276 288 261 X1 25 31 45 60 65 72 80 84 75 60 50 38 X2 24 21 24 25 25 26 25 25 24 25 25 23 Fit a multiple linear regression model to these data. 4. Derive the normal equations for the regression line of Y on X Y=aX+b by least square method.
UNIT-2
1.Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions. Impoverished, standard, enriched, super enriched. After two months, the rats were tested on a variety of learning measures(including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure(overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below. Compute the appropriate test for the data provided below. F-critical value: 5.29 Impoverished Standard Enriched super-enriched 22 17 12 8 19 21 14 7 15 15 11 10 24 12 9 9 18 19 15 12
1. What is your computed answer?
2. What would be the null hypothesis in this study?
3. Interpret your answer?
2. The following table gives three independent samples from a normal population. Test whether the means are equal at 5% level Sample 1 19 23 18 21 20 Sample 2 17 19 21 20 25 Sample 3 19 23 25 17 19
UNIT-3
1. a) What are the objectives of the Discriminant Analysis? b) What are the application areas of Discriminant Analysis?
2. a) What are the two assumptions underlying in Discriminant Analysis? b) Compare and contrast Discriminant Analysis and Multiple Regression Analysis.
3. a) Answer the following i) Define Discriminant Analysis. ii) What is the scope of Discriminant Analysis? b) How is Discriminant Analysis performed in SPSS? Explain briefly.
UNIT-4
1.The standard deviation of three variables Total dry matter(X1) Green dry matter(x2) and percent edible green(X3) are 0.27, 0.99 and 1.26 respectively. The correlation matrix was |1 .11 .04 .11 1 .86 .04 .86 1 Find the covariance matrix. Perform principal component analysis. What are the components accounting for 75% of the total variation?
2. Find principal components for the following data. X1 X2 X3 X4 25.0 86 66 186.49 24.9 84 66 124.34 25.4 77 55 98.79 24.4 82 62 118.88 22.9 79 53 71.88 7.7 86 60 111.96 25.1 82 58 99.74 24.9 83 63 100.16 24.9 78 56 62.38 24.3 85 67 154.40 24.6 79 61 112.71 24.3 81 58 79.63 24.6 81 61 125.59 24.1 85 64 99.87 24.5 84 63 143.56 24 81 61 114.97
UNIT-5
1. a) How is Factor Analysis used in data reduction? Explain with simple example. What is the need for rotation in Factor Analysis. b) What are the steps involved in Factor Analysis for SPSS. Explain with an example by taking dummy data. c) Are Factor Analysis and Principal Component Analysis the same? Justify.
2.a) In factor analysis find the relationship between the factor k and the characteristics p for the model y=μ+Λf+ε where y=(Yi)p x 1, μ-(μi)p x 1, Λ=(λij)p x k , f=(fi)k x 1 , and ε=(εi) p x 1. b) Obtain the factor loading matrix λ=(λ11,λ21,λ31)’ for the one factor model with 3 characteristics for which the covariance matrix Σ= 5 2 1 2 3 0.5 1 0.5 2
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I attached second semester Model Question Paper ....
DATA ANALYTICS
UNIT-1
1.Given the data X1: 10 5 7 19 11 18 X2: 2 3 3 6 7 9 X3: 15 9 3 25 7 13 Fit the Multiple linear regression models in matrix form; specifically calculate the least squares estimates β, the fitted values y, the residuals ε, and the residual sum of squares ε’ε.
2. Define Regression. Scores made by the students in a class in the mid- term and final examination are given here. Develop a regression equation which may be used to predict final examination scores from the mid-term score and also find the estimated final score of a student for mid-term score is 50. STUDENT: 1 2 3 4 5 6 7 8 9 10 MID-TERM: 98 66 100 96 88 45 76 60 74 82 FINAL: 90 74 98 88 80 62 78 74 86 80
3. The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature(X1), the number of days in the month(X2). The past year’s historical data are available and are presented in the following table. Y 240 236 270 274 301 316 300 296 267 276 288 261 X1 25 31 45 60 65 72 80 84 75 60 50 38 X2 24 21 24 25 25 26 25 25 24 25 25 23 Fit a multiple linear regression model to these data. 4. Derive the normal equations for the regression line of Y on X Y=aX+b by least square method.
UNIT-2
1.Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions. Impoverished, standard, enriched, super enriched. After two months, the rats were tested on a variety of learning measures(including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure(overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below. Compute the appropriate test for the data provided below. F-critical value: 5.29 Impoverished Standard Enriched super-enriched 22 17 12 8 19 21 14 7 15 15 11 10 24 12 9 9 18 19 15 12
1. What is your computed answer?
2. What would be the null hypothesis in this study?
3. Interpret your answer?
2. The following table gives three independent samples from a normal population. Test whether the means are equal at 5% level Sample 1 19 23 18 21 20 Sample 2 17 19 21 20 25 Sample 3 19 23 25 17 19
UNIT-3
1. a) What are the objectives of the Discriminant Analysis? b) What are the application areas of Discriminant Analysis?
2. a) What are the two assumptions underlying in Discriminant Analysis? b) Compare and contrast Discriminant Analysis and Multiple Regression Analysis.
3. a) Answer the following i) Define Discriminant Analysis. ii) What is the scope of Discriminant Analysis? b) How is Discriminant Analysis performed in SPSS? Explain briefly.
UNIT-4
1.The standard deviation of three variables Total dry matter(X1) Green dry matter(x2) and percent edible green(X3) are 0.27, 0.99 and 1.26 respectively. The correlation matrix was |1 .11 .04 .11 1 .86 .04 .86 1 Find the covariance matrix. Perform principal component analysis. What are the components accounting for 75% of the total variation?
2. Find principal components for the following data. X1 X2 X3 X4 25.0 86 66 186.49 24.9 84 66 124.34 25.4 77 55 98.79 24.4 82 62 118.88 22.9 79 53 71.88 7.7 86 60 111.96 25.1 82 58 99.74 24.9 83 63 100.16 24.9 78 56 62.38 24.3 85 67 154.40 24.6 79 61 112.71 24.3 81 58 79.63 24.6 81 61 125.59 24.1 85 64 99.87 24.5 84 63 143.56 24 81 61 114.97
UNIT-5
1. a) How is Factor Analysis used in data reduction? Explain with simple example. What is the need for rotation in Factor Analysis. b) What are the steps involved in Factor Analysis for SPSS. Explain with an example by taking dummy data. c) Are Factor Analysis and Principal Component Analysis the same? Justify.
2.a) In factor analysis find the relationship between the factor k and the characteristics p for the model y=μ+Λf+ε where y=(Yi)p x 1, μ-(μi)p x 1, Λ=(λij)p x k , f=(fi)k x 1 , and ε=(εi) p x 1. b) Obtain the factor loading matrix λ=(λ11,λ21,λ31)’ for the one factor model with 3 characteristics for which the covariance matrix Σ= 5 2 1 2 3 0.5 1 0.5 2
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