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In the linear regression model Y_{t}=B_{1}+B_{2}X_{t}+u_{t}, OLS estimation yielded b_{1}=2.5 and...

Question:

In the linear regression model {eq}Y_{t}=B_{1}+B_{2}X_{t}+u_{t} {/eq}, OLS estimation yielded {eq}b_{1}=2.5 {/eq} and {eq}b_{2}=3 {/eq}.

Suppose, instead of using {eq}X_{t} {/eq} and {eq}Y_{t} {/eq}, we use {eq}X_{t}^{'}=10X_{t} {/eq} and {eq}Y_{t}^{'}=5Y_{t} {/eq}.

Calculate the new coefficients, their standard errors, and the R-squared for the transformed model.

Ordinary Least Square (OLS):

The ordinary least square is a type of linear regression that estimates the unknown parameters that explain the relationship between the dependent and independent variable(s). Under some assumption, the OLS estimates are the base linear unbiased estimates (BLUE).

Answer and Explanation: 1

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The coefficient of the transformed regression are:

  • {eq}b_{1}'=5\times b_{1}=5 \times 2.5 =12.5 \\ \displaystyle b_{2}'=\frac {5}{10}\times...

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Simple Linear Regression: Definition, Formula & Examples

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Chapter 8 / Lesson 2
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Simple linear regression is a great way to make observations and interpret data. In this lesson, you will learn to find the regression line of a set of data using a ruler and a graphing calculator.


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