The data below show the number of years it took for selected technological innovations to spread to 25% of the U.S. population. The data are also in file XR17062. For y = years to spread and x = years past 1800 (e.g., the code for 1975 is 175), generate a scatter diagram and apply an appropriate polynomial model to fit the data. Does there appear to be any relationship between the variables? How much of the variation in dissemination time is explained by the model? Using your model, predict how long it will take for a major technological invention that is invented in 2010 to spread to 25% of the U.S. population.

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Years t Year Code Invention Spreac Home electricity (1873) Telephone (1875) Automobile (1885) 73 46 75 35 85 55 Radio (1906) Television (1925) 106 22 125 26 VCR (1952) Microwave oven (1953) 152 34 153 30 Personal computer (1975) Cellular phone (1983) 175 15 183 13