Exercise 4 gave data on x = BOD mass loading and y = BOD mass removal. Values of relevant summary quantities are

Data From Exercise 4 

a. Obtain the equation of the least squares line.
b. Predict the value of BOD mass removal for a single observation made when BOD mass loading is 35, and calculate the value of the corresponding residual.
c. Calculate SSE and then a point estimate of σ. 

d. What proportion of observed variation in removal can be explained by the approximate linear relationship between the two variables?
e. The last two x values, 103 and 142, are much larger than the others. How are the equation of the least squares line and the value of R² affected by deletion of the two corresponding observations from the sample? Adjust the given values of the summary quantities, and use the fact that the new value of SSE is 311.79.

Transcribed Image Text:

X y y A study to assess the capability of subsur- face flow wetland systems to remove bio- chemical oxygen demand (BOD, a measure of organic matter in sewage) and various other chemical constituents resulted in the accompanying data on x = BOD mass loading (kg/ha/d) and y = BOD mass removal (kg/ha/d) ("Subsurface Flow Wetlands A Performance Evaluation,' Water Environ. Res. 1995: 244-247). 3 4 30 26 8 7 35 21 10 8 37 9 11 8 38 31 13 10 44 30 16 11 103 75 27 16 142 90