Q4 (8 points) One would like to study the relationship between the sepal length, sepal width and the species of iris using logistic regression. There are two species, setosa(-1), versicolor(=0). The output is given in the table below. Coefficients: Estimate Std. Error z value Pr(>Izl) (Intercept) -18.3069 4.5467 -4.026 5.66e-05 *** Sepal. Length -0.8447 Sepal.Width 7.8053 0.2848 1.6568 4.711 2.47e-06 *** Signif. codes: 0*** 0.001 *** 0.01 * 0.05 0.1'1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 138.629 on 99 Residual deviance: 59.734 on 97 AIC: 65.734 degrees of freedom degrees of freedom Number of Fisher Scoring iterations: 6 (a) Interpret sepal.Length based on the estimated value and test the hypothesis Ho: Sepal.Length = 0 against H₁ Sepal Length 0 at the significance level 0.05. (b) Calculate the R-square and the maximum likelihood (L(B)). (c) Use the G-statistic to test the hypothesis Ho ẞSepal.Length 0.05. Sepal. Width 0 at the significance level ẞSepal.Width (d) The following is a testing set of 10 new observations. Based on part (a), calculate the estimated probabilities of being setosa for the testing set. If the cutoff values are chosen at 0.4, what is the proportion of correct classification? Sepal. Length Sepal. Width Species.type 5.36 3.5 1 6.67 3.0 1 4.93 3.2 1 5.24 3.1 1 6.43 3.6 1 9.73 3.2 0 8.09 3.2 0 9.38 3.1 0 5.85 2.3 0 7.01 2.8 0
Q4 (8 points) One would like to study the relationship between the sepal length, sepal width and the species of iris using logistic regression. There are two species, setosa(-1), versicolor(=0). The output is given in the table below. Coefficients: Estimate Std. Error z value Pr(>Izl) (Intercept) -18.3069 4.5467 -4.026 5.66e-05 *** Sepal. Length -0.8447 Sepal.Width 7.8053 0.2848 1.6568 4.711 2.47e-06 *** Signif. codes: 0*** 0.001 *** 0.01 * 0.05 0.1'1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 138.629 on 99 Residual deviance: 59.734 on 97 AIC: 65.734 degrees of freedom degrees of freedom Number of Fisher Scoring iterations: 6 (a) Interpret sepal.Length based on the estimated value and test the hypothesis Ho: Sepal.Length = 0 against H₁ Sepal Length 0 at the significance level 0.05. (b) Calculate the R-square and the maximum likelihood (L(B)). (c) Use the G-statistic to test the hypothesis Ho ẞSepal.Length 0.05. Sepal. Width 0 at the significance level ẞSepal.Width (d) The following is a testing set of 10 new observations. Based on part (a), calculate the estimated probabilities of being setosa for the testing set. If the cutoff values are chosen at 0.4, what is the proportion of correct classification? Sepal. Length Sepal. Width Species.type 5.36 3.5 1 6.67 3.0 1 4.93 3.2 1 5.24 3.1 1 6.43 3.6 1 9.73 3.2 0 8.09 3.2 0 9.38 3.1 0 5.85 2.3 0 7.01 2.8 0
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Q4 (8 points) One would like to study the relationship between the sepal length, sepal width and the species
of iris using logistic regression. There are two species, setosa(-1), versicolor(=0). The output is given in the
table below.
Coefficients:
Estimate Std. Error z value Pr(>Izl)
(Intercept)
-18.3069 4.5467 -4.026 5.66e-05 ***
Sepal. Length -0.8447
Sepal.Width 7.8053
0.2848
1.6568
4.711 2.47e-06 ***
Signif. codes: 0*** 0.001 *** 0.01 * 0.05 0.1'1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 138.629 on 99
Residual deviance: 59.734 on 97
AIC: 65.734
degrees of freedom
degrees of freedom
Number of Fisher Scoring iterations: 6
(a) Interpret sepal.Length based on the estimated value and test the hypothesis Ho: Sepal.Length = 0 against
H₁ Sepal Length 0 at the significance level 0.05.
(b) Calculate the R-square and the maximum likelihood (L(B)).
(c) Use the G-statistic to test the hypothesis Ho ẞSepal.Length
0.05.
Sepal. Width 0 at the significance level
ẞSepal.Width
(d) The following is a testing set of 10 new observations. Based on part (a), calculate the estimated
probabilities of being setosa for the testing set. If the cutoff values are chosen at 0.4, what is the
proportion of correct classification?
Sepal. Length Sepal. Width Species.type
5.36
3.5
1
6.67
3.0
1
4.93
3.2
1
5.24
3.1
1
6.43
3.6
1
9.73
3.2
0
8.09
3.2
0
9.38
3.1
0
5.85
2.3
0
7.01
2.8
0
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