TENEO INTERNATIONAL SCHOOL     SUBJECT:  iLIFE SMARTS      DATE: 26 JULY 2021     TIME: 85 MINUTES + 5 MINUTES SUBMISSION TIME     MARKS: 50 MARKS     EXAMINER: R. ISMAIL     MODERATOR:  N. du TOIT         INSTRUCTIONS   1. The answers you provide to the question paper, must be your own, original work. No copying from any source is allowed. No marks will be awarded for work that is copied   2. Read all the questions carefully.   3. Use the mark allocation as a guide to how much information is required in your answers.   4. Answer all the questions – do not leave any blank.  

6.5 Discuss TWO strengths and TWO weaknesses of democracy. (4)

Question 3: Bike Data – Goodness of Fit (3a) 3 pts – Evaluate whether the deviance residuals are approximately normally distributed by producing a QQ plot and histogram of the deviance residuals. Based on these plots, what assessment can you make about the goodness of fit of model1? (3b) 2 pts – Perform a goodness-of-fit statistical test for model1 using the deviance residuals and significance level 0.05. Provide the null and alternative hypotheses, test statistic, p-value, and conclusion in the context of the problem.  (3c) 3 pts – Why might a Poisson regression model not be a good fit? Provide two reasons. How can you try to improve the fit in each situation? Do not apply the recommendations.

Question 7: Wine Data – Regularized Regression (7a) Using wine_data_train, conduct ridge regression with quality as the binary response variable and all other variables in wine_data_train as the predicting variables. (7a.1) 3 pts – Use 10-fold cross validation on the misclassification error to select the optimal lambda value. What optimal lambda value did you obtain? Hint: Make sure to change the value of type.measure in order to perform cross validation on the misclassification error. If needed, you can take a look at the help file by typing ?cv.glmnet. (7a.2) 1.5 pts – Fit a glmnet object with nlambda = 100. Call it ridge_model.  (7a.3) 1 pt – Display the estimated coefficients at the optimal lambda value.

Multiple Choice Questions 32-33 The following table shows the R output of a logistic regression model, where the variables Sepal.Length, Sepal.Width,  Petal.Length, and Petal.Width are predictors and the variable virginica is the response. Using the following R output from a fitted logistic regression model, answer Questions 32 and 33.   Call:glm(formula = virginica ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, family = binomial, data = iris)Deviance Residuals:      Min        1Q    Median        3Q       Max  -2.01105  -0.00065   0.00000   0.00048   1.78065  Coefficients:             Estimate Std. Error z value Pr(>|z|)  (Intercept)   -42.638     25.708  -1.659   0.0972 .Sepal.Length   -2.465      2.394  -1.030   0.3032  Sepal.Width    -6.681      4.480  -1.491   0.1359  Petal.Length    9.429      4.737   1.990   0.0465 *Petal.Width    18.286      9.743   1.877   0.0605 .—Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1(Dispersion parameter for binomial family taken to be 1)    Null deviance: 190.954  on 149  degrees of freedomResidual deviance:  11.899  on 145  degrees of freedomAIC: 21.899

Question 8: Wine Data – Prediction (8a) 6 pts – Using model3, all_subsets_model, stepwise_model, and ridge_model, give a binary classification to each of the rows in wine_data_test, with 1 indicating a good quality wine. Use 0.5 as your classification threshold.  (8b) 4.5 pts – For each model, display its accuracy, sensitivity, and specificity metrics. Hint: confusionMatrix() from the caret package could be used to calculate these metrics. (9b.1) Which model has the largest accuracy? (9b.2) Which model has the largest sensitivity?(9b.3) Which model has the largest specificity? (8c) 1 pt – In this context, should sensitivity or specificity matter more? Explain. Hint: Remember that sensitivity is the proportion of all 1s in the test set that are correctly classified as 1s, while specificity is the proportion of all 0s in the test set that are correctly classified as 0s. (8d) 1 pt – Based on 8b and 8c, which model performed the best?

Which methods below can be applied for variable selection when ? Select ALL correct answers. Note: is the number of predicting variables and is the sample size.

Question 5 – Wine Data – Full Model (5a) 2 pts – Using wine_data_train, fit a logistic regression model with quality as the response variable and all other variables as predicting variables. Include an intercept. Call it model3. Display the summary table for the model.  (5b) 2 pts – Conduct a multicollinearity test on model3. Using a VIF threshold of 10, what can you conclude? (5c) 2 pts – Estimate the dispersion parameter for model3. Does overdispersion seem to be a problem in this model?

In Poisson regression, when the model is a good fit, the sum of squared deviance residuals approximately follows the

Question 1: Bike Data – Exploratory Analysis (1a) 2 pts – Using bike_data_train, create a histogram of the variable bikes. Based on this plot, what generalized linear regression model(s) discussed in this course could be used to model this response variable? Explain. (1b) 2 pts – Using bike_data_train, create a scatterplot of bikes versus each numeric predicting variable (high_temp, low_temp, and precipitation) (3 scatterplots total). Do these variables appear useful in predicting the number of bikes crossing the Brooklyn Bridge on a given day? Include your reasoning.