Practise fitting and comparing linear, quadratic, exponential, power or sine regressions, evaluating residuals and R², and judging prediction limits.
Juliet is a sociologist who wants to investigate if income affects happiness amongst doctors. This question asks you to review Juliet's methods and conclusions.
Juliet obtained a list of email addresses of doctors who work in her city. She contacted them and asked them to fill in an anonymous questionnaire. Participants were asked to state their annual income and to respond to a set of questions. The responses were used to determine a happiness score out of 100 . Of the 415 doctors on the list, 11 replied.
Juliet wants to create a model to predict how changing annual income might affect happiness scores. To do this, she assumes that annual income in dollars, X, is the independent variable and the happiness score, Y, is the dependent variable.
She first considers a linear model of the form
Find the coefficient of determination for each of the two models she considers.
for quadratic model: R2=0.659(0.659145…)
A1
for linear model: R2=0.311(0.311056…)
Note: Follow through from their r value from part (c)(ii).
Hence compare the two models.
Juliet decides to use the coefficient of determination to choose between these two models.
EITHER
quadratic model is a better fit to the data / more accurate
OR
quadratic model explains a higher proportion of the variance