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 = METHOD-rotational and non rotational method of planting PINCOME 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. C. 10- OB- 06- 04- 02- 00. SIZE X₁ 5 Shermat 8 2 1.2 1.5 Predicted 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. RATIO X₂ 0.5 0.75 0.8 0.8 0.75 METHOD X₁ Rotational Rotational Predicted Non-rotational Rotational Non-rotational 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. P= 1.34 +0.034X₁ +0.049 X₂-0.041 X₁ +0.029X, +0.011 Xs +0.08X6- Explain the regression coefficients b₁, b, and be 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 ß₂ = 0.1 and the size of the farm is 1000 hectares.