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QuizMultiple Choice

Linear Regression Methods — Quiz

Question 1 • Algebra II

The table shows the size of outdoor decks x in square feet, and the estimated dollar cost to construct them y x y x squared x y 100 600 10 comma 000 60 comma 000 144 850 20 comma 736 122 comma 400 225 1 comma 300 50 comma 625 292 comma 500 324 1 comma 900 104 comma 976 615 comma 600 400 2 comma 300 160 comma 000 920 comma 000 the sum from to of x is equal to 1 comma 193 the sum from to of y is equal to 6 comma 950 the sum from to of x squared is equal to 346 comma 337 the sum from to of x is equal to 2 comma 010 comma 500 Which regression equation correctly models the data?

Answer
A
y is equal to 5 point 7 1 x plus 27 point 6
B
y is equal to 5 point 8 3 x plus 17
C
y is equal to 5 point 7 1 x plus 29
D
y is equal to 5 point 8 3 x minus 1 point 0 4

Explanation

For the least-squares regression line, the slope is [5(2,010,500) − (1,193)(6,950)] ÷ [5(346,337) − (1,193)²], which is approximately 5.71. The intercept is [6,950 − 5.71(1,193)] ÷ 5, approximately 27.6. Therefore, the regression equation is y = 5.71x + 27.6, choice A.

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