Mrs. Ruby is a researcher, she conducts research on the decay of the quality of bananas. She proposed 4 models: M 1 : y = − 2 x + 15 M 2 : y = 1.5 x + 15 M 3 : y = − 2 x + 13 M 4 : y = − 1 x + 15 In these models, y indicates a quality factor (or decay factor) which is dependent on x number of days. The value of y varies between 0 and 15, where the value 15 denotes that the fruit has no decay and y = 0 means it is completely decayed. While formulating a model she has to make sure that on the 0 t h day the banana has no decay. The quality factor (or decay factor) y values on x t h day are shown in the table below. x y 4 8 5 5 6 4 7 2 What is the SSE value of the best fit model till two decimal places?
Answers
Given:
x y
4 8
5 5
6 4
7 2
predicted models
y = -2x+15
y = 1.5x+15
y = -2x+13
y = - x+15
To Find: SSE value of the best fit model till two decimal places
Solution:
x y y = -2x+15 | d | d² =SSE
4 8 7 1 1
5 5 5 0 0
6 4 3 1 1
7 2 1 1 1
3
x y y = 1.5x+15 | d | d² =SSE
4 8 21 13 169
5 5 22.5 17.5 306.25
6 4 24 20 400
7 2 25.5 23.5 552.25
1427.5
x y y = -2x+13 | d | d² =SSE
4 8 5 3 9
5 5 3 2 4
6 4 1 3 9
7 2 -1 3 9
31
x y y = - x+15 | d | d² =SSE
4 8 11 3 9
5 5 10 5 25
6 4 9 5 25
7 2 8 6 36
95
best fit model y = -2x+15 and SSE value is 3
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