Urban population estimation using satellite images. Refer to the Geographical Analysis (January 2007) study that demonstrated the use of satellite image maps for estimating urban population. A first-order model for census block population density (y) was fit as a function of proportion of block with lowdensity residential areas (x1) and proportion of block with high-density residential areas (x2). Now consider a second-order model for y.
(a) Write the equation of a quadratic model for y as a function of x1.
b) Identify the β term in the model that allows for a curvilinear relationship between y and x1.
(c) Suppose that the rate of increase of population density (y) with proportion of block with low-density areas (x1) is greater for lower proportions than for higher proportions. Will the term you identified in part b be positive or negative? Explain.