In the 1950s, Franco Modigliani developed the Life Cycle Hypothesis. One tenet of this hypothesis is that income varies with age. The following data represent the annual income and age of a random sample of 15 adult Americans.

(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?
(b) Find the quadratic regression equation yÌ… = b0 + b1x + b2x2.
(c) Draw a residual plot against the fitted values, x, and x2. Also, draw a boxplot of the residuals. Are there any problems with the model?
(d) Interpret the coefficient of determination.
(e) Does the F-test indicate that we should reject H0: β1 = β2 = 0? Is either coefficient not significantly different from zero?
(f) Construct and interpret 95% confidence and prediction intervals incomes for an age of 45 years.

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Age, r Income, y Age, r Income, y 25,490 25 47 41,398 27 26,910 52 36,474 54 32 32,141 38,934 37 35,775 35,893 57 42 36,451 62 30,629 38,093 22,708 42 67 47 36,266 72 20,506