To find SYY (the total sum of squares), we need to calculate the sum of the squared differences between each observed y value and the mean y value.
First, calculate the mean of the y values:
mean_y = (7 + 6.2 + 9 + 9.5 + 8.5 + 7.8 + 11.2 + 295 + 297.5 + 291 + 289 + 301 + 293 + 286.5) / 14
mean_y = 2119 / 14
mean_y = 151.3571
Next, calculate the squared differences for each y value:
(7 - 151.3571)^2 = (-144.3571)^2 = 20860.682653
(6.2 - 151.3571)^2 = (-145.1571)^2 = 21086.193735
(9 - 151.3571)^2 = (-142.3571)^2 = 20243.180653
(9.5 - 151.3571)^2 = (-141.8571)^2 = 20114.577633
(8.5 - 151.3571)^2 = (-142.8571)^2 = 20408.774143
(7.8 - 151.3571)^2 = (-143.5571)^2 = 20596.411051
(11.2 - 151.3571)^2 = (-140.1571)^2 = 19641.386293
(295 - 151.3571)^2 = (143.6429)^2 = 20614.258943
(297.5 - 151.3571)^2 = (146.1429)^2 = 21376.558183
(291 - 151.3571)^2 = (139.6429)^2 = 19471.814623
(289 - 151.3571)^2 = (137.6429)^2 = 18936.470943
(301 - 151.3571)^2 = (149.6429)^2 = 22385.245943
(293 - 151.3571)^2 = (141.6429)^2 = 20058.024943
(286.5 - 151.3571)^2 = (135.1429)^2 = 18249.032943
Summing these squared differences:
SYY = 20860.682653 + 21086.193735 + 20243.180653 + 20114.577633 + 20408.774143 + 20596.411051 + 19641.386293 + 20614.258943 + 21376.558183 + 19471.814623 + 18936.470943 + 22385.245943 + 20058.024943 + 18249.032943
SYY = 276377.636963
Therefore, SYY is approximately 276377.637.
Researchers at the University of the Free State investigated a model for rate of seed germination. In one experiment, the alfalfa seeds were placed in a specially constructed germination chamber. Eleven hours later, the seeds were examined and the change in free energy recorded. The results for seeds germinated at seven different temperatures are given in the next table. The data were used to fit a linear regression model, with y = change in free energy and x = temperature.
CHANGE IN FREE ENERGY
TEMPERATURE
7
6.2
9
9.5
8.5
7.8
11.2
295
297.5
291
289
301
293
286.5
Determine: SYY
35.8143
16.5571
602 265.5
2 053
149.9286
1 answer