Inference and Simple Regression Assignment

Instructions

This case offers an opportunity to use simple regression to study predictors of subjective wellbeing (SWB). Economists and others are increasingly interested in measures of SWB as a tool for decision making and policymaking that goes beyond pecuniary measures to factor all of the three Ps of thetriple bottom line: profit, people, and planet.

For this assignment, you will read the provided case (downloadable below) and write a report based on the provided questions.

OMIS 3200 Quantitative Methods Inference and Simple Regression Assignment Graeme Warren1 Leavey School of Business [email protected] Overview This case offers an opportunity to use simple regression to study predictors of sub- jective wellbeing (SWB). Economists and others are increasingly interested in measures of SWB as a tool for decision making and policymaking that goes beyond pecuniary measures to factor all of the three Ps of the triple bottom line: profit, people and planet. Introduction Angus Deaton, 2015 winner of the 2015 Nobel Prize, in Economics, in an article with Arthur Stone, wrote: "Economists, as well as psychologists and philosophers, have become increasingly interested in self-reported measures of well-being, what they mean, and whether they might be used for policymaking. This interest parallels a renewed aware- ness of the limitations of standard measures of GDP (and allied measures), as well as a wish to redirect measurement away from GDP in an era when growth rates are diminishing across much of the rich world. Various subjective well- being (SWB) measures have been used to provide new insights and to capture a number of difficult-to-measure phenomena, such as the trade-off between in- flation and unemployment, the costs of air pollution, or the values attached to environmental amenities." This case offers an opportunity to investigate predictors of evaluative measures of SWB (such as the Cantril ladder, also known as the “self-anchoring striving scale”) using simple regression and meta analysis. Deaton and Stone distinguish between evaluative (such as the Cantril ladder) and hedonic measures of wellbeing, writing: We look at two different ways of measuring well-being, an evaluative measure, the Cantril ladder, and a hedonic measure, daily happiness. The former invites respondents to rate their lives on a “ladder” with 11 steps, marked from 0, which represents the worst possible life for you, to 10, which represents the best possible life for you. Answering such a question requires the respondent to think about his life and interpret the question. We also look at a dichotomous 1License: Creative Commons CC-BY-SA 4.0. Document Date: March 6, 2018. http://www.economist.com/node/14301663 https://en.wikipedia.org/wiki/Angus_Deaton https://www.nytimes.com/2015/10/13/business/angus-deaton-nobel-economics.html?_r=1 http://www.princeton.edu/~deaton/downloads/Deaton_Economic_Analysis_of_Subjective_Well_Being.pdf http://www.gallup.com/seniorscientists/177248/arthur-stone.aspx http://www.gallup.com/poll/122453/understanding-gallup-uses-cantril-scale.aspx https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=14&cad=rja&uact=8&ved=0ahUKEwjqj-XI4rTXAhVkl1QKHV_bDu8QFghgMA0&url=https%3A%2F%2Fcreativecommons.org%2Flicenses%2Fby-sa%2F4.0%2Flegalcode&usg=AOvVaw0KxLsClrjwwBibTzCsIPm7 OMIS 3200 QUANTITATIVE METHODS 2 measure in response to the question “Did you experience a lot of happiness yesterday?” This is one of a number of hedonic questions, which should be distinguished from the evaluative question in the ladder. Hedonic questions do not require the cognitive effort required to answer evaluative questions, they refer to different aspects of experience, and they often have different correlates. For example, hedonic measures are uncorrelated with education, vary over the days of the week, improve with age, and respond to income only up to a threshold. Evaluative measures remain correlated with income even at high levels of income, are strongly correlated with education, are often U-shaped in age, and do not vary over the days of the week (Stone et al. 2010; Kahneman and Deaton 2010). The important distinction between evaluative and hedonic well-being renders unhelpful the portmanteau use of the term “happiness,” or, indeed, subjective well-being. The Cantril scale is a survey measure of the Gallup World Poll and has been used to develop the World Happiness Report. The 2017 edition was published on International Day of Happiness, March 20, 2017. The 2015 and 2016 editions are available online. The 2016 report ranked (in order) Denmark, Switzerland, Iceland, Norway and Finland as the world’s happiest countries. The 2017 report ranked (in order) Norway, Denmark, Iceland, Switzerland and Finland as the world’s happiest countries. The US dropped to 14th spot from 13th in 2016 (up from 15th spot in 2015). The US was behind Canada in 2015, 2016 and 2017 and behind Mexico in 2015. Togo, Syria and Burundi round out the 157-country list in 2017, as they did in 2016. Check out this interactive dashboard to get a feel. Data The data is taken from the OECD Better Life Index and World Happiness Report. Definitions of the variables in the OECD data set are available. Also see the FAQ of the World Happiness Report. The SWB field in the OECD (respectively, WHR) data is called "Life Satisfaction" (respectively, "Life Ladder.") Assignment The overall objective of this assignment is to use simple regression modeling and meta analysis to find six good stand-alone predictors of SWB. The assignment details are as follows. 1. For each of your six OECD or WHR predictors, develop five single-year simple re- gression models on OECD or WHR data, selecting either the OECD variable "Life Satisfaction" or WHR variable "Life Ladder" as the dependent variable. That is, you could develop simple regressions on WHR data for each of the predictors of "Life Lad- der" for each year of data that you consider. We are using data from five separate years in order to obtain five models for each predictor for meta analysis. 2. Document your regression results in a table showing the model coefficient (b1), R2, p-value, and confidence interval of the slope. http://worldhappiness.report/ http://worldhappiness.report/wp-content/uploads/sites/2/2015/04/WHR15.pdf http://worldhappiness.report/wp-content/uploads/sites/2/2016/03/HR-V1_web.pdf http://www.oecdbetterlifeindex.org/ https://stats.oecd.org/Index.aspx?DataSetCode=BLI http://worldhappiness.report/ http://www.oecd.org/statistics/OECD-Better-Life-Index-2016-definitions.pdf http://worldhappiness.report/faq/ OMIS 3200 QUANTITATIVE METHODS 3 3. Perform a meta analysis (using the "Single r" tab in the Excel-based ESCI Meta Analysis tool - available as a free download) of each predictor using the five year mod- els. Include the "synthesis forest plot, synthesized confidence interval, and associated p-value in your report for each predictor you study. 4. Use your results to select six predictors that you think are the "best," and moti- vate your choices. Discuss the requirements for regression (linearity, normality, ho- moskedasticity, and independence) for each and include scatterplots for each of the six predictors you select. ] Report Guidelines 1. You are free to use any software to do the analysis, although I strongly recommend using Minitab 18 (on a Windows machine) or Minitab Express (on a Mac). 2. Case reports must be individually written, but collaborative discussion and analysis is highly encouraged. 3. Review the grading rubric. 4. Essential: develop and defend at least one thesis. Clearly articulate your thesis and its primary support in the executive summary. 5. Submit reports in Word or PDF formats. Also submit your spreadsheet and/or Minitab files. 6. Bring all practical considerations to bear. Develop reasonable assumptions and estimates where necessary. 7. Write cases in English prose (paragraphs and sentences). Create and appropriately label and reference tables for data and figures for charts. Hard page-count maximum: 5 pages (everything included). Pick your battles wisely! No cover pages! Page format- ting: 1 inch margins all around, single-spaced 12 pt font. Suggestion for document organization: write introduction, analysis and conclusion sections. Rubric Category Weight Are five regression models appropriately developed and documented for each predictor? 30% Are synthesis forest plots, confidence intervals and p-values presented for each predictor? 25% Are six predictors selected and appropriately motivated? 25% Does the report appropriately argue a central thesis? 20% http://routledgetextbooks.com/textbooks/9781138825529/student.php http://routledgetextbooks.com/textbooks/9781138825529/student.php Overview Introduction Data Assignment Report Guidelines Rubric