Select the answer below that best describes a dependent variable: It is the variable that we are using to predict the independent variable (response/explanatory, the z variable) It is the variable that we are trying to predict (outcome/response, the y variable) It is the variable that we are using to predict the dependent variable (predictor/explanatory, the x variable) It is the variable that is the quantitative variable (numeric whole/numeric decimal, the w variable)

Select the answer below that best describes a dependent variable: It is the variable that we are using to predict the independent variable (response/explanatory, the z variable) It is the variable that we are trying to predict (outcome/response, the y variable) It is the variable that we are using to predict the dependent variable (predictor/explanatory, the x variable) It is the variable that is the quantitative variable (numeric whole/numeric decimal, the w variable)

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1. Suppose that a set of samples x1, x2, ..., xn, all real numbers, are drawn i.i.d. from the same distribution. Also assume that this distribution is a Gaussian distribution, which can be represented as N(u, o²). Write a function that accepts a set of samples and returns the MLE estimator for u. NOTE: The code below will be evaluated by a Python 2.7 interpreter. def mle(samples): pass Run Reset Once your function is correct, your will receive a submission code that you should input into the answer field. Enter answer here 2. In the previous question, you were asked to write a function for an estimator of a parameter of a distribution. Is the result of this function, an estimator, a random variable? Yes No
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Size of sample space A six-sided dice is rolled, a five-sided dice is rolled and a three-sided dice is rolled. Considering this as a probability experiment, what is the size of the sample space? An Event In the context of the probability experiment just described (a 6-sided, a 5-sided, and a 3-sided dice thrown): Consider the event in which two face- up numbers on the three dice add to 10. What is the size of this set? Save Reset
PART A Roll a single standard six-sided die 36 times and tabulate your results (i.e., number of l's, number of 2's,..., number of 6's). Calculate the mean, variance and standard deviation of your data. PART B Roll a pair of standard six-sided dice 36 times and tabulate your results (i.e., number of 2's, number of 3's, number of 12's). Calculate the mean, variance and standard deviation of your data. ****
You build a model predicting blood pressure as a function of three variables: weight (numeric) age (numeric) income (categorical: low, medium, high) You first specify your model as: blood pressure ~ age * income + weight How many parameters (k) does your model have? (Remember, we do not count the grand mean in k) You change the above model specification to be: blood pressure ~ age * income + weight * income How many parameters does your model have now? You change your model to include the three-way interaction (which, remember, includes all two-way interactions and main effects, too!) Your model now looks like this: blood pressure ~ age * income * weight How many parameters does your model have now?
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If two variables X and Y are independent, learning the values of Y does not change the prediction of X. True False
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In bivariate regression, the regression coefficient will be equal to rXY when: