Decision Tree and Statistical Methods Quiz

What criteria were used to make the first split in the decision tree?

• Age

• Tumor Size

• Lymph Nodes

• Tumor Marker

If a patient is 65 years old, has a tumor size of 3.5 cm, a tumor marker level of 24, what is the most likely diagnosis according to the decision tree?

• Benign

• Malignant

• Uncertain

• None of above

For patients with Tumor Marker ≥ 12.14, how does age affect the diagnosis?

• Patients older than 60 are more likely to be diagnosed with benign tumors.

• Patients older than 60 are more likely to be diagnosed with malignant tumors.

• Age does not impact the diagnosis when Tumor Marker ≥ 12.14.

• Age impacts the diagnosis only when Tumor Size is ≥ 4.067 cm.

Using the k-Nearest Neighbors (k-NN) algorithm with k=5 and the Euclidean distance, determine the class label for the test instance.

• The test instance will be classified as positive.

• The test instance will be classified as negative.

• The test instance cannot be classified without additional information.

• The test instance will have an ambiguous class label.

The plot above shows the variable importance for the Heart dataset, where importance is computed using mean increase in mean squared error (MSE). Based on the plot, which of the following variables are the three most important?

• Ca, Thal, ChestPain

• Age, Chol, Slope

• Fbs, RestECG, ExAng

• MaxHR, Oldpeak, RestBP

Imagine you are conducting a simulation to estimate the probability of rolling a sum of 7 with two six-sided dice. You decide to run the simulation multiple times to get a reliable estimate. Why is it important to set a random seed before starting your simulations?

• To make the simulation run faster and save time

• To ensure that you can reproduce the same results if you run the simulation again

• To add more randomness to the results and increase variability

• To remove any potential bias in the simulation outcomes

You have collected a dataset of the heights (in cm) of 30 students in a classroom: You decide to use the bootstrap method to estimate the 95% confidence interval for the mean height of the students. Which of the following steps would you take first to implement the bootstrap method?

• Calculate the mean height of the original dataset and use it as your estimate.

• Randomly sample with replacement from the original dataset to create a new bootstrap sample.

• Calculate the standard deviation of the original dataset.

• Plot a histogram of the original dataset to visualize the distribution.

Once you have generated multiple bootstrap samples, how would you calculate the 95% confidence interval for the mean height?

• Take the mean of the original dataset and add/subtract the standard error.

• Use the 2.5th and 97.5th percentiles of the bootstrap sample means to define the interval.

• Use the minimum and maximum values of the original dataset.

• Calculate the mean of the bootstrap samples and use that as the point estimate.

A researcher conducts a permutation test to compare the mean recovery times of two groups (10 patients on a new drug, 10 on a placebo). They follow these steps: pool all recovery times, shuffle the data, compute the difference in means, repeat 10,000 times, and calculate the p-value. Which of the following statements is false?

• The p-value is the proportion of shuffled differences greater than or equal to the observed difference for a two-sided test.

• The null hypothesis assumes no effect of the drug on recovery time.

• Permutation tests require data to be normally distributed in both groups.

• Permutation tests are non-parametric and don't rely on distributional assumptions.

A statistician is using the classical approach to estimate the standard error of the sample mean, assuming the data is normally distributed. However, after analyzing the data, the statistician realizes that the normality assumption may not hold, and the estimator's sampling distribution cannot be derived analytically. To address these limitations, the statistician decides to use the bootstrap algorithm instead. Which of the following best explains why the bootstrap algorithm is needed in this scenario, and how it works?

• The bootstrap algorithm generates random samples from a theoretical normal distribution and estimates the standard error using these samples.

• The bootstrap algorithm repeatedly samples from the original dataset with replacement to create multiple 'bootstrap samples,' computes the statistic of interest for each sample, and uses the distribution of these statistics to estimate the standard error without relying on distributional assumptions.

• The bootstrap algorithm applies only when data is normally distributed and gives a parametric estimate of the standard error based on known sampling distributions.

• The bootstrap algorithm simulates new data based on the estimated parameters of the original dataset and derives the sampling distribution assuming the underlying data is normally distributed.