The table shows the size of outdoor decks (x) in square feet, and the estimated dollar cost to construct them (y).xyx2xy10060010,00060,000144850 20,736122,4002251,300 50,625292,5003241,900 104,976615,6004002,300 160,000920,000∑x=1,193​∑y=6,950∑x2=346,337∑xy=2,010,500Which regression equation correctly models the data?

Use the least-squares regression formulas with the five data points: the slope is [5(2,010,500) − (1,193)(6,950)] ÷ [5(346,337) − (1,193)²] ≈ 5.71. The means are x̄ = 1,193 ÷ 5 = 238.6 and ȳ = 6,950 ÷ 5 = 1,390, so the intercept is 1,390 − 5.71(238.6) ≈ 27.6. Therefore, the regression equation is y = 5.71x + 27.6, choice D.

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