Asked by angela vidal on Jun 27, 2024
Verified
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.
Least Squares Estimate
A statistical technique that determines the line of best fit for a model by minimizing the sum of the squares of the vertical differences (residuals) between the observed values and the values predicted by the model.
Intercept
In the context of mathematical graphs and equations, it refers to the point where a line or curve crosses an axis.
- Determine the least squares estimates of the slope and intercept in linear regression.
Verified Answer
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.
Learning Objectives
- Determine the least squares estimates of the slope and intercept in linear regression.
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