Growing Beans Project Broad Beans LECTURER: MS. GRACE Done by: Faisal, Hussain, Karthik and Faiz 11 - Nov, 2011
Jun 20, 2015
Growing Beans ProjectBroad Beans
LECTURER: MS. GRACE
Done by: Faisal, Hussain, Karthik and Faiz
11 - Nov, 2011
BROAD BEAN
Broad bean is a specie of bean native to north Africa and southwest Asia
They are dark brown outside and light yellow inside
They are sweet and soft and easily digested
The most popular use of broad beans in western world is for sprouting. Interestingly, the sprouts contain vitamin C that is not found in the bean
NUTRITIONMature seeds, rawNutrition value per 100 g (3.5 oz)
Energy 1,452 kJ (347 kcal)Carbohydrates 62.62 gSugars 6.60 gDietary fiber 16.3 gFat 1.15 gProtein 23.86 gVitamin C 4.8 mg (8%)Calcium 132 mg (13%)Magnesium 189 mg (51%)Phosphorus 367 mg (52%)Potassium 1246 mg (27%)Sodium 15 mg (1%)
Boiled mung beans
Nutrition value per 100 g (3.5 oz)
Energy 441 kJ (105 kcal)Carbohydrates 19.15 gSugars 2.00 gDietary fiber 7.6 gFat 0.38 gProtein 7.02 gVitamin C 1.0 mg (2%)Calcium 27 mg (3%)Magnesium 0.298 mg (0%)Phosphorus 99 mg (14%)Potassium 266 mg (6%)Sodium 2mg (0%)
WITHOUT FERTILIZER (TABLE)
Days Height (cm)
1 122 173 224 245 246 25.57 268 269 26
10 27
SCATTER PLOT
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Height
Height
LINEAR REGRESSION
y = 1.3667x + 15.433R² = 0.7365
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12
Height
Height
QUADRATIC REGRESSION
y = -0.2879x2 + 4.5333x + 9.1R² = 0.9456
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Height
Height
CUBIC REGRESSION
y = 0.0552x3 - 1.1981x2 + 8.7315x + 4.3667R² = 0.9906
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Height
Height
Poly. (Height )
QUARTIC REGRESSION
y = -0.0028x4 + 0.1161x3 - 1.6438x2 + 9.9495x + 3.4167
R² = 0.9912
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Height
Height
EXPONENTIAL REGRESSION
y = 15.289e0.0691x
R² = 0.6642
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12
Height
Height
LOGARITHMIC REGRESSION
y = 6.3795ln(x) + 13.314R² = 0.9407
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Height
Height
THE BEST FIT MODEL
Model R2
Linear 0.7365
Quadratic 0.9456
Cubic 0.9906
Quartic 0.9912
Exponential 0.6642
Logarithmic 0.9407
The model which fits the best is Quartic Regression
BEST FIT QUARTIC REGRESSION
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = − 0.00276807 x⁴ + 0.11606449 x³ − 1.64379371 x² + 9.94949495 x + 3.41666667R² = 0.991162300876723
Height
Height Polynomial (Height )
Y=-0.0028x4 + 0.1161x3 – 1.6438x2 + 9.9495x + 3.4167
Domain : (0,16.7198)
Range : (0,34.0827)
X-intercept : (22.4967,0)
Y-intercept : (0,3.4167)
Properties of the Best fit Function
Predictionsf(11)=27.4957
f(13)=30.0589
f(15)=32.8917
f(16)=33.8407
f(17)=34.0405
f(20)=25.6867
As the predictions shown, the height of mung beans will continue growing till the 16th day, and then it will decrease. In the real life, this prediction is unreasonable. It is impossible for plants to grow lower and lower as time passes. Therefore, It proves that the domain is correct, which is xϵ(0, 16.7198 ) when y is maximized.
Days Height (cm)
1 13
2 19
3 23
4 25
5 25
6 26
7 26.5
8 26.5
9 26.5
10 27.5
With Fertilizer (Table)
Linear Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = 1.24848484848485 x + 16.9333333333333R² = 0.700402720010563
HeightLinear (Height)Linear (Height)
Quadratic Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = − 0.280303030303031 x² + 4.33181818181819 x + 10.7666666666667R² = 0.926355053806034
HeightPolynomial (Height)Polynomial (Height)
Cubic Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = 0.0627428127428127 x³ − 1.31555944055944 x² + 9.10654623154624 x + 5.38333333333331R² = 0.992583578367892
HeightPolynomial (Height)Polynomial (Height)
Quartic Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = − 0.0059731934731936 x⁴ + 0.194153069153072 x³ − 2.27724358974361 x² + 11.7347513597514 x + 3.33333333333327R² = 0.995784897745682
HeightPolynomial (Height)Polynomial (Height)
Exponential Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = 16.7013589480336 exp( 0.0605718189364812 x )R² = 0.62882041699912
HeightExponential (Height)Exponential (Height)
Logarithmic Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = 5.92468411077541 ln(x) + 14.8511126825703R² = 0.924562897624409
HeightLogarithmic (Height)Logarithmic (Height)
The best fit model
The quartic regression is a best fit model in this case as r² closest to 1.
Model R2
Linear 0.7004
Quadratic 0.9264
Cubic 0.9926
Quartic 0.9958
Exponential 0.8802
Logarithmic 0.9246
Best fit Quartic Regression
0 2 4 6 8 10 120
5
10
15
20
25
30
f(x) = − 0.00597319 x⁴ + 0.1941531 x³ − 2.2772436 x² + 11.734751 x + 3.3333333R² = 0.995784897745682
HeightPolynomial (Height)Polynomial (Height)
Y= -0.006x4+ 0.1942x³ – 2.2772x² + 11.735x + 3.3333
Properties of the Best fit Function
Domain : (0, 11.3554)
Range : (0, 27.5462)
X-intercept : (16.8444,0)
Y-intercept : (0, 3.3333)
Predictionsf(11)=27.5113
f(13)=26.3329
f(15)=18.6633
f(16)=10.3573
f(17)=-2.3039
f(20)=-79.2467
In the real life, this prediction is unreasonable. It is impossible for plants to grow lower and lower as time passes. Moreover, the height appears a negative value as the prediction of the growing situation in the 17th day, which is totally impossible.
Therefore, we restricted the domain to (0, 16.8444) in that the height will be zero at this x value. As a matter of fact, our broad beans were stopped growing on the 11th day and were dead on the 14th day.
Conclusion
Based on our analysis, the quartic regression is the best fit model for the growth of our mung beans with and without fertilizer.
In terms of the 10 days’ growing, the broad beans with fertilizer grew higher than those without fertilizer.
Theoretically, the broad beans should have continued growing. However, in the real case, they were stopped growing since the 11th day.
We planted a lot of mung beans this time whereby the height was hard to measure. Furthermore, the death of our broad beans was probably speeded up by the crowded mung beans. Next time, we’d better plant a few broad beans in the same pot.
Thank You