Answer: 67.315
We start by using the formula for the slope of the least squares regression line:
m = (nΣ(xy) - ΣxΣy) / (nΣ(x^2) - (Σx)^2)
where n is the number of data points, and Σ denotes the sum of the indicated quantities.
Substituting the given values, we get:
m = (4(1x9 + 2x7 + 3x3 + 4x2) - (1+2+3+4)(9+7+3+2)) / (4(1^2 + 2^2 + 3^2 + 4^2) - (1+2+3+4)^2)
= (-39) / 20
= -1.95
Next, we use the formula for the y-intercept:
b = (Σy - mΣx) / n
Substituting again, we get:
b = (9+7+3+2 - (-1.95)(1+2+3+4)) / 4
= 6.425
So the equation of the least squares regression line is:
y = -1.95x + 6.425
To compute the minimum square error, we use the formula:
SSE = Σ(y - yhat)^2
where SSE stands for sum of squared errors, y is the actual y-value of each data point, and yhat is the predicted y-value on the regression line.
Substituting the given values, we get:
SSE = (9 - (-1.95)(1) + 6.425)^2 + (7 - (-1.95)(2) + 6.425)^2 + (3 - (-1.95)(3) + 6.425)^2 + (2 - (-1.95)(4) + 6.425)^2
= 67.315
Therefore, the minimum square error is approximately 67.315.