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Questiоn 2 Multiple Lineаr Regressiоn (61 pоints) Use trаinDаta for this question 11 points2a) A linear regression model is created using "annual_yield_kg" as response variable and the following variables as predictors: watering_frequency, growing_medium, sunlight_hours. It is named as 'model1'. The summary is displayed. Answer the following questions based on the model summary. i)(4 points) After controlling for watering_frequency and growing_medium, how does a one-unit increase in sunlight_hours affect the expected annual_yield_kg? Interpret the coefficient in context. ii)(3 points) Can you determine which predictor is "most important" simply by comparing the magnitudes of their coefficients? Explain why or why not. iii)(4 points) What percentage of the variability in annual_yield_kg is explained by model1? Is the remaining unexplained variability large enough to suggest that important predictors may be missing? 17 points 2b) (2 points) Create a full linear regression model using all the predictors in the dataset “trainData”. Call it model2. Display the summary. i)(4 points) Interpret the coefficient for roof_area_m2. What would be the expected change in annual yield for a 100 m² increase in roof area? ii)(3 points) What does the relatively small difference between R² and adjusted R² suggest about the predictors? iii)(3 points) Interpret the coefficient of growing_mediumHydroponic with reference to the reference category. State the assumptions. iv)(5 points) What does residual standard error represent? Compare the RSE values of model1 and model2. Explain your conclusion. 16 points 2c) Model Diagnostics The following diagnostic plots for model2 are provided: a residuals-versus-fitted-values plot, a Q-Q plot, and a histogram of the residuals. i)(4 points) Based on the residuals-versus-fitted values plot, which assumption is being questioned? According to the plot shown, explain why this pattern is or is not problematic for ordinary least squares regression. ii)(4 points) Based on the normal Q-Q plot and histogram, what assumption about the errors can you assess? According to the plots shown, explain whether the assumption appears to be satisfied and why this pattern is or is not problematic for ordinary least squares regression. iii)(4 points) Suppose the residuals have two extreme positive observations, but removing them makes the Q-Q plot nearly normal. Would you remove them? iv)(4 points) A model has excellent R2, low RSE, and statistically significant predictors, but its residuals show both heteroscedasticity and severe non-normality. Can you still claim that the model is a good model? Defend your answer. 8 points 2di)(3 points) Calculate the 95% confidence intervals for all the coefficients of the full model created in Question 2b. 2dii)(5 points) Compare the confidence intervals for irrigation_systemManual and irrigation_systemSprinkler. What can you conclude about their effects relative to the reference category? 9 points 2ei)(4 points) Use the Cook’s distance to count outliers in the data based on model2. Plot the Cook's distance for each observation. Any observation with a Cook’s distance larger than 4/n should be considered an outlier. State clearly the number of outliers. ii)(5 points) After identifying observations with unusually large Cook’s distances in model2, refit the model after excluding these observations. Compare the coefficient estimates, statistical significance with those from the original model. Do any substantive conclusions about the predictors change? What does the comparison reveal about the influence and stability of model2?