1. Regression analysis

Can anyone help with this problem?

Would appreciate any partial or full input. Thanks.

Suppose that we estimate a model:

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \epsilon_i
$

but the true model is

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \beta_2 \cdot experience_i + \epsilon_i
$

What will the consequences be for our regression estimates? Are these serious; is this something we have to care about? Assume instead that it is the way around; thus, that the true model is.

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \epsilon_i
$

but we are estimating

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \beta_2 \cdot experience_i + \epsilon_i
$

what are the consequences on our regression estimates. Are these serious consequences; do we need to care about this? Note: No calculations are needed!

2. Originally Posted by Jiffy22
Can anyone help with this problem?

Would appreciate any partial or full input. Thanks.

Suppose that we estimate a model:

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \epsilon_i
$

but the true model is

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \beta_2 \cdot experience_i + \epsilon_i
$

What will the consequences be for our regression estimates? Are these serious; is this something we have to care about? Assume instead that it is the way around; thus, that the true model is.

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \epsilon_i
$

but we are estimating

$
wage_i = \beta_0 + \beta_1 \cdot grade_i + \beta_2 \cdot experience_i + \epsilon_i
$

what are the consequences on our regression estimates. Are these serious consequences; do we need to care about this? Note: No calculations are needed!
You are given true model and estimated model.

From your true model, you will have the mean and standard deviation based on the size of the population, N.

Using the true model, estimated model, and standard deviation, you will get the confidence limit.

Whether it's serious or not, that will depend on the resulting percent of confidence, of which is the function of population and the standard deviation.

Note: I don't know what you are given, but I must assume that $\epsilon _{i}$denotes possible error, i=1,2,3,...N
Whether it denotes errors or not, you have a 3-dimensional center points and moments, where each point is ( $wage_{i},grade_{i},\epsilon _{i}$)