Cars with catalytic converters
A quadratic model was applied to motor vehicle toxic emissions data collected over 15 recent years in Mexico City (Environmental Science and Engineering, September 1, 2000). The following equation was used to predict the percentage (y) of motor vehicles without catalytic converters in the Mexico City fleet for a given year
(x): yˆ = 325,790 - 321.67x + 0.794x2.
(a) Explain why the value βˆ0 = 325,790 has no practical interpretation.
(b) Explain why the value βˆ1 = -321.67 should not be interpreted as a slope.
(c) Examine the value of βˆ2 to determine the nature of the curvature (upward or downward) in the sample data.
(d) The researchers used the model to estimate ‘‘that just after the year 2021 the fleet of cars with catalytic converters will completely disappear.'' Comment on the danger of using the model to predict y in the year 2021.