Hi guys!

My question is like this.

The regression specification is:

$y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$

where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$.

I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients.

Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3.

Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$.

My question: Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant?

If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$?

Thank your so much!

My question is like this.

The regression specification is:

$y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$

where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$.

I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients.

Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3.

Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$.

My question: Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant?

If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$?

My question is like this.

The regression specification is:

$y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$

where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$.

I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients.

Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3.

Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$.

My question: Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant?

If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$?

Thank your so much!

Hi guys!

My question is like this.

The regression specification is:

$y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$

where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$.

I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients.

Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3.

Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$.

My question: Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant?

If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$?

Thank your so much!

My question is like this. The regression specification is:  $y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$ where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$. I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients. Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3. Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$. My question:  Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant? If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$? Thank your so much!

My question is like this.

The regression specification is: 

$y=\delta_{1}D_{1}+\delta_{2}D_{2}+\delta_{3}D_{3}+\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}x_{3}+\epsilon$

where $D_{i}$ denotes dummy for each one of three categories, $x_{i}$ interaction between $D_{i}$ and independent variable $x$.

I want to test $b_{1}=b_{2}=b_{3}$. $b_{i}$ is the estimated coefficient of $x_{i}$. After test, I will combine interaction terms for the categories not showing significantly different coefficients.

Each category has different sample size. Category 1 have much more samples than category 2, and category 2 more than category 3.

Estimates show that $b_{1}$ and $b_{2}$ is significant (from zero), but $b_{3}$ not. I think the small sample size of category 3 could explain insignificance of $b_{3}$.

My question:  Is it meaningful (or right) to do joint test $b_{1}=b_{2}=b_{3}$ when $b_{3}$ is insignificant?

If the test $b_{1}=b_{2}=b_{3}$ can not be rejected at e.g 5% level but $b_{1}$ and $b_{3}$ is significantly different, could I say no significant difference among $x_{1}$, $x_{2}$ and $x_{3}$? 

Thank your so much!