# Finding a confidence interval for a parameter of regression given two variable variances

Given an equation $Y_i=0.1+0.3x_i+e_i$, I am asked to calculate a 95% confidence interval for $Y_i$ when $x=0$. So I have an equation $Y_i=0.1+e_i$, and I know that standard error of 0.1 is 0.005, while SE of $e_i=1.178$, and expected value of $e_i$=0. I have 25 observations, so 23 DF. How can I calculate a 95% confidence interval for this? At first I was going to do 0.1 plus/minus appropriate t score $\times$ 0.005, but I don't know how to include the variation of $e_i$ into the equation, also.

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