Using the fitted regression model, estimate the average change in cry time for infants with severe pain versus those without severe pain, holding group constant. Provide a 95% confidence interval for this estimate.
My question: What holding group constant means?
When we say "holding group constant," it means that we are keeping the group variable at a fixed level or not allowing it to change. In the context of the question, it means that we want to estimate the average change in cry time for infants with severe pain compared to those without severe pain while keeping the other variables (such as the group variable) constant.
To estimate this average change, we can use a fitted regression model. In this case, the model has been already fitted, and it takes into account various predictors (or independent variables) that may affect cry time, such as pain level, group, and potentially other factors. By controlling for these variables, we can isolate the effect of severe pain on cry time while holding the group constant.
To get the estimated average change, you would need to look at the coefficient for the severe pain variable in your fitted regression model. This coefficient represents the estimated average change in cry time associated with severe pain, holding the group constant.
As for the 95% confidence interval, it represents a range of values within which we can be 95% confident that the true average change in cry time for infants with severe pain versus those without severe pain (holding the group constant) falls. It is calculated based on the standard errors of the regression coefficients and the t-distribution.
To calculate the confidence interval, you would need to use the standard error of the coefficient for severe pain from your regression model as well as the t-value associated with a 95% confidence level. The formula for calculating the confidence interval is:
Confidence interval = estimated coefficient ± (t-value * standard error)
With this calculation, you will get a range of values that provides an estimation of the average change in cry time for infants with severe pain versus those without severe pain, while holding the group constant, along with a level of confidence that the true value falls within that range.