Numerous attempts have been made to understand happiness. Because there is no unique way to quantify it, researchers often rely on surveys to capture a subjective assessment of well-being. One study finds that holding everything else constant, people seem to be least happy when they are in their 40s (Psychology Today, April 27, 2018). Another study suggests that money does buy happiness, but its effect diminishes as incomes rise above $75,000 a year (Money Magazine, February 14, 2018). Consider survey data of 100 working adults’ self-assessed happiness on a scale of 0 to 100, along with their age and annual income. A portion of the data is shown in the accompanying table

a. Estimate and interpret a regression model for Happiness based on Age, Age² , and ln(Income). 

b. Predict happiness with Income equal to $80,000 and Age equal to 30, 45, and 60 years. 

c. Predict happiness with Age equal to 60 and Income equal to $25,000, $75,000, $125,000.

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Happiness 69 83 ⠀ 79 Age 49 47 ⠀ 31 Income 52000 123000 ⠀ 105000