Question

True or false: at the 5% level of confidence the intercept is significantly different from 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

At the 5% level of confidence the intercept is significantly different from zero: False

Explanation:

Null Hypothesis H₀: Intercept = 0 (Intercept is not significantly different from zero)

Alternate Hypothesis H_a: Intercept ≠ 0 (Intercept is significantly different from zero)

P-value corresponding to Intercept is 0.082583. Since p-value is greater than α = 0.05. So we fail to reject null hypothesis. This, intercept is not significantly different from zero at 5% level of confidence. Thus, statement given is False