How Long Should it Take to Dig a Trench?
An Example of Least Squares Regression and Transformations
This dataset contains the lengths of 15 trenches and the time it took
to dig each of them. Output from an unidentified software package is
included as well.
IND. VAR DEP. VAR
FEET MINUTES
30 2 Regression Output:
70 6.8 Constant -9.8825
270 51.4 Std Err of Y Est 32.637
79 12 R Squared 0.662906
135 18 No. of Observations 15
450 64.4 Degrees of Freedom 13
150 17.5
215 35.8 X Coefficient(s) 0.310238
65 11.5 Std Err of Coef. 0.061358
63 23.2
63 21.5
460 216
187 75
42 5.9
20 4
TOTALS
2299 565 AVG. = 0.245759 MIN/FOOT
Questions to Consider:
- Which variable is the response? Which is the explanatory variable?
- The output contains the fit of the least squares regression line for the
data. What is the equation of the line?
- Construct a scatterplot of data. Is a line an appropriate model for these
data? Why or why not?
- Transformations are sometimes used to improve the fit of a regression
model. Try some transformations on these data and examine whether there is
improvement in the quality of the fit.
- A utility company is planning to dig a trench that is 125 feet long.
About how long do you expect it to take to dig this trench?