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Question 1 The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE-farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X₁ = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X₁ = METHOD-rotational and non rotational method of planting P = INCOME - the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.3 2.1 SIZE X₁ 5 8 2 1.2 1.5 AGE X₂ 20 100 80 30 11 RATIO X₂ 0.5 0.75 0.8 0.8 0.75 METHOD X₂ Rotational Rotational Pedal Non-rotational Rotational Non-rotational 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed. Study the plots and answer the questions that follows.

Question 1 The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE-farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X₁ = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X₁ = METHOD-rotational and non rotational method of planting P = INCOME - the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.3 2.1 SIZE X₁ 5 8 2 1.2 1.5 AGE X₂ 20 100 80 30 11 RATIO X₂ 0.5 0.75 0.8 0.8 0.75 METHOD X₂ Rotational Rotational Pedal Non-rotational Rotational Non-rotational 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed. Study the plots and answer the questions that follows.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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a. C. Sample Quantiles 1.0- 08- 02- 00- Predicted Theoretical Quantiles 3 Predicted Diagnose each of the possible problems that are displayed in the plots. If applicable also mention a formal way to test that it is indeed a problem. Also, when a problem is diagnosed, provide a possible remedial measure to remedy the problem. 1.2. In order to prepare the dataset for modelling, it became clear that RATIO repeats with similar values. The analyst decided to regard them also as categorical variables. Amend the dataset fully in order to build a regression model. Use an ascending order in the coding structure. 1.3. Show the new amended data set and formulate the regression model that must be estimated. Apply all the changes done to the dataset in Question 1.2 and give the regression function. 1.4. The estimated response function is obtained using the coding structure of Question 1.2. 8 = 1.34 +0.034X₂ + 0.049 X₂-0.041 X3 +0.029X4 +0.011 X5 +0.08x6. Explain the regression coefficients b₁,b, and b6- 1.5. Find the fitted response function for the rotational METHOD of farming on a farm with RATIO of 0.8. 1.6. Refer to Question 1.5. The analyst has a suspicion that there is interaction between the size and the age of the farm if the method of farming is rotational and the field/land ratio is 0.8. Give the response function to show this. Also, interpret b₂ if ß3 = 0.1 and the size of the farm is 1000 hectares.
Transcribed Image Text:a. C. Sample Quantiles 1.0- 08- 02- 00- Predicted Theoretical Quantiles 3 Predicted Diagnose each of the possible problems that are displayed in the plots. If applicable also mention a formal way to test that it is indeed a problem. Also, when a problem is diagnosed, provide a possible remedial measure to remedy the problem. 1.2. In order to prepare the dataset for modelling, it became clear that RATIO repeats with similar values. The analyst decided to regard them also as categorical variables. Amend the dataset fully in order to build a regression model. Use an ascending order in the coding structure. 1.3. Show the new amended data set and formulate the regression model that must be estimated. Apply all the changes done to the dataset in Question 1.2 and give the regression function. 1.4. The estimated response function is obtained using the coding structure of Question 1.2. 8 = 1.34 +0.034X₂ + 0.049 X₂-0.041 X3 +0.029X4 +0.011 X5 +0.08x6. Explain the regression coefficients b₁,b, and b6- 1.5. Find the fitted response function for the rotational METHOD of farming on a farm with RATIO of 0.8. 1.6. Refer to Question 1.5. The analyst has a suspicion that there is interaction between the size and the age of the farm if the method of farming is rotational and the field/land ratio is 0.8. Give the response function to show this. Also, interpret b₂ if ß3 = 0.1 and the size of the farm is 1000 hectares.
Question 1 The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ỹ = INCOME - the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 SIZE X₁ a. 5 8 2 1.2 1.5 AGE X₂ Predicted 20 100 80 50 11 b. RATIO X₂ 0.5 Standardized Residual 0.75 0.8 0.8 0.75 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed. Study the plots and answer the questions that follows. METHOD X₂ Rotational Rotational Predicted Non-rotational Rotational Non-rotational
Transcribed Image Text:Question 1 The income of farmers depends on various factors. To predict the income of the next year, a study was undertaken and data was gathered considering as many as possible factors that might influence the yearly income. Regression methods are used to create such a prediction function, that is, we want to predict the profit for the next year. The following were determined. X₁ = SIZE - farm size recorded x 1000 hectares X₂ = AGE - how long the farm has been in operation in years X = RATIO - the ratio of land size to field size recorded as 0.5, 0.75, 0.8 and 0.9 X4 = METHOD - rotational and non rotational method of planting Ỹ = INCOME - the income per year recorded in x R 1 000 000.00 The partial dataset is as follows INCOME Y 1.3 2.4 3.2 1.5 2.1 SIZE X₁ a. 5 8 2 1.2 1.5 AGE X₂ Predicted 20 100 80 50 11 b. RATIO X₂ 0.5 Standardized Residual 0.75 0.8 0.8 0.75 1.1. The analyst did some exploratory analysis and below are some of the residual plots he constructed. Study the plots and answer the questions that follows. METHOD X₂ Rotational Rotational Predicted Non-rotational Rotational Non-rotational
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