Data has been gathered involving the average ratings over the course of treatment for patients undergoing radiotherapy:
•Number of symptoms (as nausea, sore throat)
•Amount of activity (on a 1-5 scale)
•Amount of sleep (on a 1-5 scale)
•Amount of food consumed (on a 1-3 scale)
•Appetite (on a 1-5 scale)
•Skin reaction (on a 0-3 scale)
You are asked to find a single measure ie a linear combinations of the 6 abovementioned measurements, to represent patients’ response to therapy.
Symptoms Activity Sleep Eat Appetite Skin Reaction
0.889 1.389 1.555 2.222 1.945 1
2.813 1.437 0.999 2.312 2.312 2
1.454 1.091 2.364 2.455 2.909 3
0.294 0.941 1.059 2 1 1
2.727 2.545 2.819 2.727 4.091 0
3.937 1.25 1.937 2.937 3.749 1
2.786 1.714 2.357 2.071 2 2
5.231 2.692 1.077 1.846 2.539 1
1.15 1.1 0.95 2 1 1
6.5 2.562 1.749 2.562 2.499 1
0.8 1 2.2 2.267 2.466 2
4.6 2 3 2.5 3.4 1
3.5 1.286 2.714 1.286 1.252 3
3.444 2.556 2.388 2.389 3 1
4.071 1 1 2.357 1.572 1
3.692 1 2.538 2.154 2.615 1
5.167 3 1 2.667 3.666 0
0.5 1 1 2 1 0
2.385 1.923 2.539 2.154 2.461 1
2.1 1.3 1.3 1.8 2.6 1
5 3.25 3.125 2.375 3.375 0
4.571 1.214 3.286 2.571 3.572 1
2.733 1.133 2.6 1.933 1.667 1
4.235 2.294 2.706 2.176 1.883 1
a) What multivariate tool will you use and why?
b) Use Minitab to provide the simplest linear combination of the 6 abovementioned measurements and INCLUDE your MINITAB FILE with your submission (you must provide this to receive credit). List the simplest linear model below:
b) Is the simplest linear model acceptable? Explain why/why not and provide a graph to support your view
c) How much of the data variability does this simplest model account for?
Sample Solution