Question

4- The biochemical oxygen demand (BOD) test is conducted over a period of time in days. The resulting data follow: Time (days):2 4 6 8 10 12 14 16 18 20 BOD (mg/liter): 0.6 0.7 15 1.9 2.1 2.6 2.9 3.7 3.5 3.7 3.8 (a) Test for significance of regression using o 0.01. Find the P-value for this test. What conclusions can you draw? (b) Estimate the standard errors of the slope and intercept (c) Test the hypothesis that Bo 0.

Answer 1

We use Excel to solve this problem,

The biochemical demand(BOD) is depend on the time therefore we take regression analysis by taking BOD as a dependent variable y and independent variable x.
a)
At alpha = 0.01 & P-value is 0.0000
Observe that P-value < alpha therefore model is significance to the regression.
b)
Standard error = 0.287 indicates that average distance that the observed value fall from the regression i.e. how wrong the regression model is on average using the BOD.
Slope = 0.18 indicates that as time changes by 1 days then BOD is 0.18 mg/liter
Intercept = 0.66 indicates that when wee keep days value 0 (constant) then BOD is 0.66 mg/liter
c)
Observe that p-value corresponding to intercept is 0.0033 < alpha = 0.01 therefore $\beta o\neq 0$