Review Quadratic Model

Life Cycle Hypothesis - Review

This problem will help you prepare for the Best Fit Models Quiz.  The answers are included below. 

Don't look at the answers until you complete this review problem.

         An individual's income varies with his or her age. The following table shows the median income, I, of individuals of different age groups within the United States for 2003. For each age group, let the class midpoint represent the independent variable, x. For the class "65 years and older" we will assume that the class midpoint is 69.5.

Age                 Class midpoint, x       Median Income, I

15 - 24 years                   19.5                                  $9,961

25 - 34 years                   29.5                               $30, 562

35 - 44 years                   39.5                               $39,195

45 - 54 years                   49.5                               $42,079

55 - 64 years                   59.5                               $38,915

65 years and older           69.5                               $20,363

A.   Use Desmos to draw a scatter diagram of the data. 

      Comment on the type of relationship that may exist between the two variables.

B.   Use the Desmos' regression line process to find the quadratic function of the best fit that models the relationship between age and median income.

C.   Use the function found in part (B) to determine the age at which any individual can expect to earn the most income.

D.   Use the function found in part (B) to predict the peak income earned.

E.   Graph the quadratic function of the best fit on the scatter diagram.

F.   Using the information above, answer the following questions.

      1.    The scatter points represent what type of model (linear/quadratic)?

      2.    Record your regression function below.  Record only 3 places after the decimal point.

      3.    What is the age at which any individual can expect to earn the most income?

      4.    What would be the peak income earned?  Round to the nearest dollar?

G.  After you complete this review and you don't have questions email me to access the quiz. 

------------------------------------------------