You are given the following information about y and x. ​ ​
The least squares estimate of the intercept or b₀ equals

A) 1.
B) -2.
C) 12.
D) 4.

Without knowing the specific values of x and y, we can use the least squares regression line equation:

ŷ = b0 + b1x

where b0 is the intercept and b1 is the slope. The least squares estimate of the intercept can be found by plugging in the mean of x and y:

b0 = ȳ - b1x̄

Since we don't have the specific values of x and y, we can use the information given to calculate the mean of x and y:

x̄ = /8

x̄ = 13976/8 = 1747

ȳ = x̄ - 2 = 1747 - 2 = 1745

Therefore, the least squares estimate of the intercept is:

b0 = ȳ - b1x̄

We do not have enough information about the slope b1, so we cannot calculate the exact value of b0. However, we can eliminate answer choices A and B because they are too small to be the intercept of a line that is fit to a set of data points. Answer choice D is also unlikely to be the correct answer since it is much larger than the mean of y. The best choice is C, which is a value that is reasonable for an intercept given the range of the data.