mcs3500 a2

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University of Guelph *

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3500

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Marketing

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Apr 3, 2024

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Marketing Analytics M C S 3500 _S ec. 2 ( Winter 2023) Assignment 2: Market Response Model (100 Points) Due on March 03 (by mid - night) Data: boston housing. csv – randomly sample only 406 house prices from 50 6 house prices. For all questions , use log( medv ) as outcome or dependent variable ( see data description in next page ) Multiple Linear Regression (50 points ) : Q 1 (A).

Identify most important variables using best subset algorithm to predict house prices using three model selection criteria ( RSS = residual sum of square; adjr^2 = adjusted R^2 and BIC =Bayesian information criteria). 20 points Q 1 (B). Develop a conceptual framework using important variables identified in Q 1 (A ). Also, provide descriptive statistics for the identified important variables in Q 1 (A) . (5 + 5 = 10 points ) Q 1 (C). Run multiple linear regression model with these identified variables in Q 1 (A) . Write regression equation and i nterpret any four regression coefficients.

20 points Multiple Linear Regression with Quadratic Effects (30 points ) : Q 2 (A). Run multiple regression analysis with the variables identified in Q 1 (A) with adding quadratic effects of average numbers of rooms ( rm ) and provide average marginal effects (ame) with comments. 10 points Q 2 (B). Plot and interpret prediction and average marginal effects of average number of rooms ( rm ) . 20 points Multivariate Adaptive Splines (MARS) (20 points ) : Q 3 (A). Run MARS using all variables in the housing data to investigate non - linear response patterns. Comments on your findings

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that show non - linear patterns (if exist). 15 points Q 3(B). Are the identified variables using MARS the same or different from Q 1 (A) ? Please comment , if any . 5 points Format : Generate R output s and then produce your report as a Word document ( by using knit function in Rmarkdown) . A dd your answer s or interpretation s in th at Word document. Your assignment should include ONLY necessary codes, output s , and plots that are relevant for the assignment questions.

Remove irrelevant code chunks from your Word file and rmd file . Submit the Word file as well as the R markdown (rmd) file prepared for this assignment . Useful Tips: When you prepare your R markdown file, please make sure the following chunks are added in the beginning : Chunk 1: Run this chunk to knit your outputs Chunk 2: Open Installed Packages Chunk 3: Opening and Selecting Data for your Assignment Then add necessary code chunks as required by the questions 2 The use of AI and ChatGPT is NOT permitted to prepare the assignments Assignment 2 Rubrics: Q 1 (A): (20 marks): Correct code & outputs - 12 | Model selection criteria - 8 Q 1 (B): (10 marks): Conceptual framework - 5 | Correct code for descriptive statistics - 5

Q 1 (C): (20 marks): Code - 8 | Regression equation - 4 | Interpretations of four coefficients - 8 (4*2) Q 2 (A): (10 marks): Correct code and output - 5 | Interpretation - 5 Q 2 (B): (20 marks): Correct code and output - 10 | Interpretation of prediction plot and AME plot - 10 (5*2) Q 3 (A): (15 marks): Correct code and output - 10 | Comment - 5 Q 3 (B): (5 marks): Complete answer - 5 Data De s cription : The source of Boston h ousing d ataset is the U.S. Census Service . This dataset highlight

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s the h ouse features of 506 houses in the area of Boston MA . The dataset columns represent variable names : 1. crim - per capita crime rate by town 2. zn - proportion of residential land zoned for lots over 25,000 sq. ft. 3. indus - proportion of non - retail business acres per town. 4. chas - Charles River dummy variable (1 if tract bounds river; 0 otherwise) 5. nox - nitric oxides concentration (parts per 10 million) 6. rm - average number of rooms per dwelling 7. age -

proportion of owner - occupied units built prior to 1940 8. dis - weighted distances to five Boston employment centers 9. rad - index of accessibility to radial highways 10. tax - full - value property - tax rate per $10,000 11. ptratio - pupil - teacher ratio by town 12. black - proportion of blacks by town 13. Lstat - % lower status of the population 14. medv - Median value of owner - occupied homes in $1000

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