Midterm Exam Analysis Predictive Modeling and Interpretation ITEC-621 Assignment

Midterm Exam

Information

Question i

Exam 1
ITEC 621 Predictive Analytics

Overview:

Learning objectiveL04of the MS Analytics program is for the student to:learn how to: (1) formulate a relevant business question or hypothesis; (2) search, identify and manipulate the necessary data to answer that question; (3) evaluate and select the most appropriate analytic models, methods and tools to analyze the data; and (4) formulate the respective model effectively and apply the selected methods and tools competently.(1) and (2) will be evaluated with the term project; (3) and part of (4) will be evaluated in this exam; and the remaining part of (4) will be evaluated with the homework.

Allowed and Not Allowed:Students are allowed to have notes, books, etc. They are not allowed to use any communication devices, including cellphones and tablets. Students can use their laptop or desktop computers, but only to complete the exam and to access the digital content provided for this class. Students are not allowed to use the laptop for anything else, including accessing the web, email, etc.

Material Covered:All lectures and ISLR textbook readings covered in class, up to and including non-linear models. R coding will not be covered but you need to be able to interpret plots and other outputs I prepared in R. You are allowed 1.5 hours. There are 4 questions, so you will need to pace yourself and complete each question in no more than 20 minutes.

General Instructions:

The exam contains 4 questions worth 25 points each. Each question is planned for 20 minutes, so you should plan to spend no more than that answering each question. You have 1.5 hours to complete the exam, which gives you a few extra minutes to review your answers. In each question you are presented with an analytics scenario or concept, followed by a short-answer question. This scenario will contain one or more of the following: (1) a particular problem to resolve or business question to answer with predictive analytics (important note: your goal will NOT be to solve the problem or answer discussion, but to discuss your approach to do that); (2) an analysis goal (i.e., interpretation, inference or prediction); (3) relevant exhibits, which may include things like: model summary outputs; plots; distributions; data descriptions/displays; and/or (4) important concepts covered in class that analytics professionals should know.

There are no questions on R coding, but a few R plots and outputs are included for interpretation questions. Longer responses will not necessarily earn more credit.More specific, concise, precise and correct answers will.

Q 1

Question 1

The owner of a restaurant chain has hired you to help them predict daily revenues (in thousands of $) at various restaurant locations. In his opinion, the best predictors for daily revenue are: weekday (Yes or No, with No representing weekends and holidays), month of the year (Jan, Feb, Mar, etc., reference re-leveled to Jan), advertising expenditures the prior day, average price for a 3-course meal (in $), pandemic restrictions (None, Light, Moderate or Strong; with None as the reference level) and Location (DC, NY, FL, VA and MD; reference re-leveled to NY). Since revenue and average price are non-negative variables, we logged both in an OLS model as follows:

Suppose that the predictors listed below are the only ones significant at p < 0>

Please interpret each of these effects.

Answer:

The case presented is a multinomial log linear model. Holding everything else constant on average for each $1k increase in revenue the weekday booking will increase 0.32, price will decrease by 1.8, the location DC will also decrease by -0.23 which will lead a increase of 0.47 during the month of June while decreasing the Covid restrictions by -.30.

Comments

Comment:

missing effects of categorical variables in relation to their reference level, missing log-linear/log-log interpretations of the coefficients, x&y variables are flipped in the interpretation.

Q 2

Question 2

Suppose that you fit an Ordinary Least Squares (OLS) regression model to predict revenues for a restaurant. You then go to inspect visually for possible violations of OLS assumptions of the resulting linear model and prepare two residual diagrams shown below. Based on a visual inspection of these diagrams, which OLS assumption violations would you suspect in each plot? Please explain the rationale for your answers and refer to the appropriate plot. Also, which test would you conduct to evaluate these OLS violations statistically? If the tests confirm the violation of these assumptions, discuss how would you correct for each of them.

Answer:

Based on the fact that a scatter plot and a histogram were used to test the error the following assumptions could be in violation:

The scatter plot shows a graph with some heteroscedasticy and/or serial correlation and the histogram is left skewed distribution.

The first OLS assumption that could be in violation is the assumption of a constant variance in which we have uneven residuals that cause observations with large errors to pull the regression strongly in both directions, thus increasing the variance. To fix that error we can run Weighted Least Squares.

The second violation could be the assumption that x and y have a linear relationship if not some x can be transformed to create a linear model. to correct the issue a nonlinear model can be run like a polynomial model.

The third violation would be the assumption that Y is continuous, to correct the issue we could use a generalized linear model, classify the data or run a log regression.

Comments

Comment:

Missing tests to address the OLS violations. Second graph is showing non-normality of the residuals.

Q 3

Question 3

Suppose that you are trying to specify a OLS regression model to predict Dietary Cholesterol (in milligrams or mg) in commercial packaged dinners (per serving). The predictors of interest (all in milligrams or mg per serving) are Saturated Fat (SatFat), Dairy, Unsaturated Fat (UnsFat), Sugar and Carbs. You first try all predictors in the model. You then try a Small model with only SatFat and Dairy as predictors. You then run a stepwise variable selection between the Large model and the Null model, which yields a model with only SatFat, UnsFat and Carbss significant predictors. The respective model and collinearity testing statistics for the respective models (Condition Index or CI; Variance Inflation Factors or VIFs; etc) are the following:

(*) Denotes significance levels p < 0>

anova(Small, Stepwise) p < 0>

anova(Stepwise, Large) p = 0.345

1. a) Which of the 3 models is more biased? Please explain why? Also, indicate which predictor in that model is likely to be biased.

b) Using the ANOVA tests only, which model would you select? Please explain why.

c) Using the two variable selection methods (i.e., subset selection using ANOVA and Stepwise), which of the 3 models would you select? Which of the 3 models would you select based on the collinearity diagnostics? Overall, which is the best model? Briefly explain why.

Answer:

1. a) The small model is more biased because does not reflect the true effects of the saturated fat and the other components in the milk; however,anova(Small, Stepwise)p < 0>

b) The adjusted R square of the large model has more significance with an adjusted Rsquare of 0.78, but theiranova(Stepwise, Large)p = 0.345 does not show significance. I would choosethe Stepwise Model in this case.

c)When looking at the CI of the three models has the highest CI indicating that Large model is very depended on and has the highest collinearity, so that model would be out as well. The small model has the smallest CI but it does not reflect the true effects of the saturated fat and the unsaturated fat in dairy, so that model is out of the questions. I would choose the stepwise model because 28.1<30>

Comments

Comment:

Q 4

Question 4

Suppose that you are developing a model to predict the likelihood that a person who was hospitalized for COVID will require admission into the intensive care unit (ICU). You fit a Logistic regression with the following variables as predictors: Smoker (Yes or No), Diabetis (Yes or No), LungIssues (Yes or No), Weight (in pounds, logged) and Age (catergorical, Under65, 65To75, and Over75, reference level = Under65).

1. a) Please interpret the log-odds and odds effects of each of the predictors in the model (note that the Weight predictor is logged and the Age predictor is categorical).

b) Does this model have a good explanatory power? In your answer, please make a reference to the p-values and the model deviance.

Answer:

1. a) Holding everything else constant on average the chances of one person to be hospitalize for covid, the log odds of a person having diabetes of being hospitalize increases by 0.182 and the odds increase by a factor of 1.186.

Holding everything else constant on average for a person to be hospitalize for covid, the log odds of a person who smokes of being hospitalize increase by 0.070 and the odds increase by a factor of 1.074.

Holding everything else constant on average for a person to be hospitalize for covid. The log odds of a person who has lung issues increase by 0.928 and the odds increase by a factor of 2.49.

Holding everything else constant on average for a person to be hospitalize for covid. The log odds of a person who is overweight increases by 0.042 and the odds increase by a factor of 1.042.

Holding everything else constant on average for a person to be hospitalize for covid. The log odds of a person who is between 65- and 75-years old increases by 0.071 and the odds increases by a factor of 1.972

Holding everything else constant on average for a person to be hospitalize for covid. The log odds of a person who is over 75 years old increases by 0.121 and the odds increases by a factor of 1.123.

1. b) I believe that the model has a good explanatory power, even though Rsquare was not provided. All the P-Values of the coefficients are significant by being less than 0.05, and the model hasa residual deviance of 600 and a null deviance of 1200 whichhow well the response is predicted by the model when the predictors are included.

Comments

Comment:

log(weight) interpretation should be similar to a log-log interpretation, the age interpretation is missing the reference level.

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