For a regression equation if we have the slope estimate b1

For a regression equation, if we have the slope estimate b1 = 10.03, the standard error of s.e.(b1) = 11.54, and the total number of observations is 30, what is the upper bound of a 95% confidence interval for italic beta subscript 1 ?

Solution

Note that              
              
  
Upper Bound = B1 + t(alpha) * se  

Here,

alpha = 1 - confidence level = 0.05          
              
where              
              
df =    28          
B1 = sample slope =    10.03          
t(alpha) = critical t for the confidence interval =    1.703288446          
se = standard error =    11.54          
              
Thus,              
              
          
Upper bound = B1 + t(alpha) * se   = 29.68594866   [ANSWER]