# set verbose off

/* gretl script to illustrate the perils of not including
   an intercept when running an OLS regression
*/

# create an "empty" dataset with space for 20 observations
nulldata 20

# create an artificial independent variable
x = index # 1, 2, 3, ...
# artificial standard normal error term
u = normal()

# the true parameter values: in "real life" these are unknown
# but in simulation we get to set them!
b0 = 10 # y-intercept
b1 = 1  # slope

# manufacture artificial dependent variable
y = b0 + b1*x + u

# run simple regression including a constant
ols y const x
SSR = $ess   # retrieve sum of squared residuals
TSS = sst(y) # find total sum of squares for y
# calculate R-squared manually
R2 = 1 - (SSR/TSS)
print R2
# compute and print the sum of residuals
uhat_sum = sum($uhat)
print uhat_sum

# now run OLS _without_ a constant
ols y x
SSR = $ess
TSS = sst(y)
# calculate R-squared in the standard way
R2 = 1 - (SSR/TSS)
print R2
uhat_sum = sum($uhat)
print uhat_sum