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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 X3 = 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 Ŷ = 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 a. J Standardized Residual Sample Quantiles 10- 08-> 06- 04- 02- SIZE X₁ 00- 5 8 2 1.2 1.5 Predicted S AGE X₂ Theoretical Quantiles 20 100 80 50 11 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. b. RATIO X3 Standardized Residual 0.5 0.75 0.8 0.8 0.75 METHOD X4 Predicted Rotational Rotational Non-rotational Rotational Non-rotational

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 X3 = 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 Ŷ = 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 a. J Standardized Residual Sample Quantiles 10- 08-> 06- 04- 02- SIZE X₁ 00- 5 8 2 1.2 1.5 Predicted S AGE X₂ Theoretical Quantiles 20 100 80 50 11 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. b. RATIO X3 Standardized Residual 0.5 0.75 0.8 0.8 0.75 METHOD X4 Predicted Rotational Rotational Non-rotational Rotational Non-rotational

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
Section3.CR: Chapter Review Exercises
Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...
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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. Ŷ = 1.34 + 0.034X₁ + 0.049 X₂ -0.041 X3 + 0.029X4 +0.011 X5 +0.08X6. Explain the regression coefficients b₁, b, and b. 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: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. Ŷ = 1.34 + 0.034X₁ + 0.049 X₂ -0.041 X3 + 0.029X4 +0.011 X5 +0.08X6. Explain the regression coefficients b₁, b, and b. 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.
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 X3 = 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 Ŷ = 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 a. Standardized Residual Sample Quantiles 10 -6- 15 1.0- 08- 0.6- 04- 02- SIZE X₁ 0.0- 5 8 1.2 1.5 Predicted Theoretical Quantiles 45 AGE X₂ 50 20 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. 100 80 50 11 b. Standardized Residual -41 -24 RATIO X3 -20 0.5 0.75 0.8 0.8 0.75 129 130 140 160 180 METHOD X4 Predicted Rotational Rotational Non-rotational Rotational Non-rotational
Transcribed Image Text: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 X3 = 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 Ŷ = 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 a. Standardized Residual Sample Quantiles 10 -6- 15 1.0- 08- 0.6- 04- 02- SIZE X₁ 0.0- 5 8 1.2 1.5 Predicted Theoretical Quantiles 45 AGE X₂ 50 20 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. 100 80 50 11 b. Standardized Residual -41 -24 RATIO X3 -20 0.5 0.75 0.8 0.8 0.75 129 130 140 160 180 METHOD X4 Predicted Rotational Rotational Non-rotational Rotational Non-rotational
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