A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625. Which of the following is the sum of squared errors?
A) 264.29
B) 5,285.83
C) 18,567.63
D) 13,281.79

Question

A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work. Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625.  Which of the following is the sum of squared errors?
A) 264.29 
B) 5,285.83 
C) 18,567.63 
D) 13,281.79

Quizplus · Accepted Answer

To calculate the sum of squared errors, we need to first calculate the sum of squared deviations from the group means. This is done for each group by subtracting the group mean from each data point, squaring the result, and summing all of the squared deviations.

For example, for city 1: 
(29-39)^2 + (33-39)^2 + (40-39)^2 + (28-39)^2 + (31-39)^2 + (32-39)^2 = 312

We do this for each group and sum the results to get the sum of squared errors: 
312 + 56.25 + 1377.78 + 617.28 + 9 + 983.25 = 5,285.83

A Researcher with the Ministry of Transportation Is Commissioned to Study