Recall that if we were calculating a confidence interval for
the population mean, m, the confidence
interval would be
_{}
_{} is the value that you looked up in the ttable with confidence level a and n = n  1 degrees of freedom. _{} is called the standard error.
Confidence intervals for y in regression problems are calculated with the formula
_{}
where _{}is the predicted value of y at x = 28 (this is from Part B), _{} is the value from the ttable with confidence level a and n = n  2 degrees of freedom, and_{} is the standard error for y.
The standard error is in the Regression Statistics table (the first table) that Excel generates when you do a regression analysis. If you look at the output for Example 2 that I did in class (mileage and book values of used cars), the Excel output is
SUMMARY
OUTPUT 

















Regression Statistics 








Multiple
R 
0.893417642 







R Square 
0.798195083 







Adjusted
R Square 
0.772969468 







Standard
Error 
2.178287887 







Observations 
10 
















ANOVA 









df 
SS 
MS 
F 
Significance F 



Regression 
1 
150.140495 
150.140495 
31.64224512 
0.000495522 



Residual 
8 
37.95950496 
4.744938119 





Total 
9 
188.1 
















Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 
Intercept 
56.20465646 
3.53516565 
15.89873348 
2.45239E07 
48.05254458 
64.35676833 
48.05254458 
64.35676833 
Mileage 
0.266821566 
0.047433731 
5.625144009 
0.000495522 
0.376204015 
0.157439116 
0.376204015 
0.157439116 
The standard error is _{} = 2.178287887.