Which of the following statement regarding pharmacologic tre…
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Which оf the fоllоwing stаtement regаrding phаrmacologic treatments for smoking is TRUE?
Questiоn 1 Dаtа Explоrаtiоn (25 points) Use dataset "urban_rooftop_gardens" for this question Q1a) (5 points) Create a scatterplot of roof_area_m2 against annual_yield_kg and determine whether the relationship appears linear or whether there is evidence of diminishing returns. Why should we examine a scatterplot before fitting a linear regression model? 1b)(5 points)The code for creating a boxplot comparing annual yield across the four irrigation systems is provided. Which irrigation system is associated with the highest annual yield? Compare the distributions, not just the mean yield, across irrigation systems. Why might some irrigation systems be associated with higher annual crop yields than others? 1c) (5 points) Are fertilizer_kg and watering_frequency strongly associated with each other? Why could this relationship (if strong) create a problem when both variables are later included in a regression model? 1d) The following table summarizes annual yield and yield per square meter by garden type: | Garden type | Mean yield (kg) | Mean yield per m² || ----------- | --------------: | ----------------: || Fruit | 707.74 | 2.663 || Herb | 573.82 | 2.395 || Mixed | 897.10 | 3.500 || Vegetable | 840.72 | 3.275 | di.(1 point) Which garden type has the highest average annual yield? Which has the highest average yield per square meter? dii.(2 points) Explain why the ranking based on total annual yield differs from—or may differ from—the ranking based on yield per square meter. Why might yield per square meter be a more appropriate measure when comparing gardens of different sizes? diii.(2 points) Based on these averages alone, can you conclude that Mixed gardens are statistically significantly more productive than Vegetable gardens? Explain what additional information or analysis would be needed. 1e)(5 points) Suppose fertilizer_kg has a very weak correlation with annual_yield_kg. Does that imply fertilizer has little practical importance? Describe an EDA strategy that could reveal a relationship hidden by other variables.
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?