Question

Given the following estimated regression, please give the correct magnitude of the coefficients, and provide a one sentence interpretation of the relationship between Y and X as talked about in class Wage = 15.00 + 0.28-YrsEdu. Where Wage is currently in dollars, and YrsEdu. are in years. A) Suppose we want Wages to be in thousands of dollars instead of dollars. B) Suppose we want Yrsedu. to be in terms of weeks instead of years. C) Suppose we want Wages to be in hundreds of dollars AND YrsEdu. in days (given that a year of education is only 180 days).

Answer 1

Following are the answer to the given choices:

Explanation:

In potion A:

The model, that will be formed can be defined as follows:

`\widehat{W age} = \hat b_(0) + \hat b_(1) x Y_(rs) \epsilon done \\\\ \hat B_1 = \frac{\sum_(i=1)^(n) (W_(age)i - \widehat{W age} * (Y_(rs) Edui - \widehat{Y_(rs)\epsilon})}{\int S_(yrs)\epsilon dre}\\`

`\ the \ new \ W_(age) = 10^(-3) * W_(age) \\\\\hat {B_(1 new)} = 10^(-3) \hat {B}\\\\ \hat{B_(0)} = \widehat{W age} -\hat {B_1} \bar{Y_(rs)\epsilon dus} \\\\\hat{B_(0 \ new)} = \widehat{W age} * 10^(-3) - 10^(-3) \hat {B_1} Y_(rs)\epsilon dus \\`

`= 10^(-3) \hat {B_0}\\`

`\hat B_(0 \ new) = 15 * 10^(-3) \\\hat B_(1 \ new) = 0.28 * 10^(-3) \\`

In potion B:

`\ The \ new \ Y_(rs)\epsilon dus = (Y_(rs) \epsilon dus)/(7) \\\hat b_(1 \ new) = 7 \hat b_1\\\hat b_( 0 \ new ) = \widehat{W_(age)} - 7 \hat b_1 * (\bar Y_(rs)\epsilon dus)/(7) \\\hat b_(0 \ new) = \hat B_(0)\\\hat b_(0) = 15.00 \\\hat b_(1) = 0.04 \\`

In potion C:

`\ Y_(rs)\epsilon dus \ new = (Y_(rs) \epsilon dus)/(180) \\\\\widehat{W_(age) new} = \widehat{W_(age)} * 10^(-2) \\\\\hat b_(1 \ new) = \hat b_(1) * 10^(-2) * 180 = \hat b_1 * 1.8 \\\\\ hat b_( 0 \ new ) = 10^(-2) \widehat{W_(age)} - \hat b_1 * 1.8 * (\bar Y_(rs)\epsilon dus)/(180) \\\\`

`= 10^(-2) \ \hat B_(0)\\`

`\hat b_(0 \ new) = 0.15 \\\hat b_(1 \ new) = 0.504 \\`