The resident population of the United States grew from 1910 to 2010 but the growth was not linear. The response variable is y = population in millions and, to simplify the calculations, the predictor variable is x = year - 1900.

(a) Fit a quadratic regression model y = β0 + β1x + β2x2 + e to these data.
(b) What proportion of the y variability is explained by the quadratic regression model?
(c) Test H0 : β1 = 0 versus H1 : β1 > with α = .05.

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10 30 40 50 y1.12.2 106 123.2 132.2 151.3 179.3 70 80 0 10010 y20332265 2487 2814 3102