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A [m] kg box is moving on a horizontal surface in the +x direction (toward the right). The coefficient of kinetic friction is [mu]. An unknown force F, parallel to the surface, is applied to the box. The velocity as a function of time is shown in the figure. Given t1 = [t1] s, t2 = [t2] s, v1 = [v1] m/s, and v3 = [v3] m/s, determine the magnitude of the force F during the time interval from t1 to t2. Express your answer in newtons.

We want to add a state category variable to the regression analysis. The state category variable has four possible answers (MO =1, FL =2, WA =3, NY = 4). In this case, we need to convert the state category variable into _________________ dummy variables for regression analysis.

What z-score represents X = 100?  Use the mean and standard deviation you just calculated in the preceding questions to arrive at your answer.  

Based on the above binary logit model in Q9, the probability of buy (i.e., P(buy=1) in the city 3 (i.e., C(city)[T.3]=1, St. Louis) is (1)___________(a. higher, b. smaller; 1 points) than that of the base group (2)__________(a. Rolla,   b. Kansas City, c. St. Louis; 2 points) at statistically (3) _______________ (a. insignificant, b. significant 10%, c. significant 5%, d. significant 1%; 1 point).

Based on the above example of the decision tree (DT) for the binary classification (0: candy 1: wine), the predicted class in the terminal node  is (1)____________(a. candy, b. wine; 2 points), and the predicted class in the terminal node  is (2)____________(a. candy, b. wine; 2 points).

Decision Tree (DF) for classification selects a feature and threshold to split feature space in each node that minimize impurity measures. Please select the two impurity measures of DT for classification:_____________ 

Let’s assume that an economist wants to investigate consumer choices for an energy saving device as follows:

Decision Tree (DF) for regression selects a feature and threshold to split feature space in each node that minimize __________________ (one answer; 4 points).

Look at the distribution for this word problem and determine if X =100 is a score that is noticeably different from the mean.  In your answer indicate 1) yes or no 2) explain why you selected your answer (i.e., back up with reasoning from facts learned in this class). 

The economist in Q1 was concerned about the confounding effect on the treatment variable (i.e., prime_card variable); therefore, the economist applied the instrument variable (IV) method using two-stage least square regression (2SLS) to mitigate bias and get a consistent estimator for the treatment effect. In particular, randomly assigned eligibility of the prime membership card for consumers (i.e., ‘prime_elegible’) is used as an instrument variable (IV). we assume that ‘prime_elegible’ is a valid instrument variable (IV). Table 1 The empirical results from OLS Table 2 The empirical result from IV with 2SLS Based on the above Tables 1 and 2, the coefficient for the prime_card in OLS is (1)____________ (number, 1 point) and the coefficient of the prime_card (i.e., the predicted prime_card in the second stage) in 2SLS is (2)___________(number, 1 point). As a result, the OLS estimator may have (3)______________ (a. downward bias (i.e., underestimate), b. upward bias (i.e., overestimate); 2 points).