You have a sample of size n = 1 with data y₁ = 2 and £₁ = 1. You are interested in the value of 3 in the regression Y = XB+ u. (Note there is no intercept.) (a) Plot the sum of squared residuals (y₁ - br₁)² as function of b. Use the range #₁ € [−2,5] for your plot, and combine all plots of this exercise in one figure. (Use any software you prefer. Excel is one option.) (b) Show that the least squares estimate of 3 is BOLS = 2.
You have a sample of size n = 1 with data y₁ = 2 and £₁ = 1. You are interested in the value of 3 in the regression Y = XB+ u. (Note there is no intercept.) (a) Plot the sum of squared residuals (y₁ - br₁)² as function of b. Use the range #₁ € [−2,5] for your plot, and combine all plots of this exercise in one figure. (Use any software you prefer. Excel is one option.) (b) Show that the least squares estimate of 3 is BOLS = 2.
Chapter3: Polynomial Functions
Section: Chapter Questions
Problem 18T
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![Problem 2. [SW 14.9]
You have a sample of size n = 1 with data y₁ = 2 and x₁ = 1. You are interested in the value of
3 in the regression Y = XB+ u. (Note there is no intercept.)
(a) Plot the sum of squared residuals (y₁ - bx₁)² as function of b.
Use the range x₁ € [−2,5] for
your plot, and combine all plots of this exercise in one figure. (Use any software you prefer.
Excel is one option.)
(b) Show that the least squares estimate of 3 is BOLS = 2.
(c) Using ARidge = 1, plot the Ridge penalty term ARidgeb² as a function of b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61ff295b-afd4-43c3-8ed2-2cc17b9c2249%2Fc263139e-9bd3-4644-ac86-af1413018b25%2Fesrmqwq_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2. [SW 14.9]
You have a sample of size n = 1 with data y₁ = 2 and x₁ = 1. You are interested in the value of
3 in the regression Y = XB+ u. (Note there is no intercept.)
(a) Plot the sum of squared residuals (y₁ - bx₁)² as function of b.
Use the range x₁ € [−2,5] for
your plot, and combine all plots of this exercise in one figure. (Use any software you prefer.
Excel is one option.)
(b) Show that the least squares estimate of 3 is BOLS = 2.
(c) Using ARidge = 1, plot the Ridge penalty term ARidgeb² as a function of b.
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