A linear regression model is fitted to the data
X 
y 
37.0 
65.0 
36.4 
67.2 
35.8 
70.3 
34.3 
71.9 
33.7 
73.8 
32.1 
75.7 
31.5 
77.9 
with x as the input variable and v as the output variable. Find β^0, β^0, and σ^2. Construct a 99% confidence interval for the expected value of the output variable when the input variable is equal to 35.