Question

Slightly different question. True or false: The effect of Well Age is significantly different than -2 at the 5% level. That's right I asked about -2 not 0, so you cannot use the p-value printed in the table because that is a test of the estimate being equal to zero. SUMMARY OUTPUT Regression Statistics Multiple R 0.98711 R Square 0.974387 Adjusted R Square 0.965849 Standard Error 47.4523 Observations 9 ANOVA df SS MS F Significance F Regression 2 513960.7 256980.4 114.1262 1.68E-05 Residual 6 13510.32 2251.72 Total 8 527471.1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept -100.805 48.43281 -2.08133 0.082583 -219.316 17.70612 -219.316 17.70612 Well Depth 11.8072 0.790904 14.92874 5.69E-06 9.87193 13.74248 9.87193 13.74248 Well Age -2.23683 0.435949 -5.13093 0.002155 -3.30356 -1.1701 -3.30356 -1.1701 True False

Answer 1

To test against

The test statistic can be written as

which under H₀ follows a t distribution with n-2 df/

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic =

and p-value

Since P-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that the coefficient of of Well Age is significantly is not different than -2.