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Question

The annual profits for a company are given in the following table, where x represents the number of years since 2002, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the profits would reach 264 thousand dollars.

Years since 2002 (x)	Profits (y)	(in thousands of dollars)
00	137137
11	150150
22	152152
33	156156

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Answer 1

Looks like the table stuttered. It should be

0 137

1 150

2 152

3 156

y = α + βx

n = 4

S_x = ∑x_i = 6

S_y = ∑y_i = 595

Mean X, M_x = 1.5

Mean Y, M_y = 148.75

S_xx = ∑(x_i-M_x)² = 5

Sum of Products, S_p = ∑(x_i-M_x)(y_i-M_y) = 29.5

β = S_p/S_xx = 29.5/5 = 5.9

α = M_y-βM_x = 148.75 - (5.9)(1.5) = 139.9

y = 139.9 + 5.9x

264 = 139.9 + 5.9x

x = (264-139.9)/5.9) = 21 years

2002 + 21 = 2023