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I have 3000 independent samples (customers) where I fit a regression model to each sample and estimate regression coefficient of interest, $B_1{_i}$ from the following model
$Y{_i} = B_0{_i} + X_1{_i}B_1{_i} + .... + e{_i}$

where $Y_i$ is sales per customer $i$.

I end up with 2 vectors of size 3000; one for the $B_1{_i}$ and another for their standard errors, $SE_1{_i}$. Some coefficients are significant and others are not.

An overall estimate of $B_1$ is needed so I use a weighted average (a weight has been derived based on prior year sales proportion out of the total) to calculate the overall estimate and use wtd.t.test from the weights package in R to test for the significance of the overall estimate.

My questions are

• Is it valid to test the significance of the overall estimate using a weighted one-sample t-test?
• Or do I need to combine the standard error estimates, $SE_1{_i}$ from all the models and calculate an overall standard error?
• And how would i calculate the overall standard error integrating the weights?

I have 3000 independent time series samples (customers) where I fit a dynamic regression model with ARIMA errors to each sample and estimate regression coefficient of interest (intervention), $B_1{_i}$ from the following model
$Y{_i} = B_0{_i} + X_1{_i}B_1{_i} + .... + e{_i}$

where $Y_i$ is sales per customer $i$.

I used ARIMA to take into account any seasonality and trend and am okay with ARIMA terms capturing other unexplained variance.

I end up with 2 vectors of size 3000; one for the $B_1{_i}$ and another for their standard errors, $SE_1{_i}$. Some coefficients are significant and others are not.

An overall estimate of $B_1$ is needed so I use a weighted average (a weight has been derived based on prior year sales proportion out of the total) to calculate the overall estimate and use wtd.t.test from the weights package in R to test for the significance of the overall estimate.

My questions are

• Is it valid to test the significance of the overall estimate using a weighted one-sample t-test?
• Or do I need to combine the standard error estimates, $SE_1{_i}$ from all the models and calculate an overall standard error?
• And how would i calculate the overall standard error integrating the weights?

I have 3000 independent samples (customers) where I fit a regression model to each sample and estimate regression coefficient of interest, $B_1{_i}$ from the following model
$Y{_i} = B_0{_i} + X_1{_i}B_1{_i} + .... + e{_i}$

where $Y_i$ is sales per customer $i$.

I end up with 2 vectors of size 3000; one for the $B_1{_i}$ and another for their standard errors, $SE_1{_i}$. Some coefficients are significant and others are not.

An overall estimate of $B_1$ is needed so I use a weighted average (a weight has been derived based on prior year sales proportion out of the total) to calculate the overall estimate and use wtd.t.test from the weights package in R to test for the significance of the overall estimate.

My questions are

• Is is it valid to test the significance of the overall estimate using a weighted one-sample t-test?
• Or do I need to combine the standard error estimates, $SE_1{_i}$ from all the models and calculate an overall standard error?
• And how would i calculate the overall standard error integrating the weights?

I have 3000 independent samples (customers) where I fit a regression model to each sample and estimate regression coefficient of interest, $B_1{_i}$ from the following model
$Y{_i} = B_0{_i} + X_1{_i}B_1{_i} + .... + e{_i}$

where $Y_i$ is sales per customer $i$.

I end up with 2 vectors of size 3000; one for the $B_1{_i}$ and another for their standard errors, $SE_1{_i}$. Some coefficients are significant and others are not.

An overall estimate of $B_1$ is needed so I use a weighted average (a weight has been derived based on prior year sales proportion out of the total) to calculate the overall estimate and use wtd.t.test from the weights package in R to test for the significance of the overall estimate.

My questions are

• Is it valid to test the significance of the overall estimate using a weighted one-sample t-test?
• Or do I need to combine the standard error estimates, $SE_1{_i}$ from all the models and calculate an overall standard error?
• And how would i calculate the overall standard error integrating the weights?