BEETLE PROBLEMA study is conducted to determine the height of a beetle which is distinctivelydifferent among other insects. The researcher randomly selected 25 insects. Eachinsect was classified as either a beetle or other and the height (in inches) wasmeasured. The data was recorded in "beetle_ex6.xlsx" inside the "beetle" tab.R Software output and Confusion Matrix:> Logit Model SummaryCoefficients:a.b.Estimate Std. Error z value Pr(>lzl)(Intercept) -6.41906 6.18612 -1.038 0.299Height0.3160.089490.08927 1.002> Wald's TestModel 1: InsectModel 2: Insect 1PHeight#Df LogLik Df Chisq Pr>Chisq)1 2 -16.62421 17.148 -1 1.04830 (Other)1 (Beetle)Total> Confusion MatrixInsect (Truevalue)PredictedProbabilityT≤0.5(0)107170.3059T>0.5(1)448Total141125Construct the logistic regression model both in terms of probability and log odds.Interpret the coefficient of the model constructed in terms of odds.Calculate the sensitivity, specificity and %accuracy of the model (# of correctlypredicted/number of samples *100)NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesisin words, test procedure, p-value, decision, & conclusion. Use α=0.05

Considering the logit model in terms of odd ratio is transformed as: lnp1-p=α+βx⇒p1-p=expα+βx The…

Answered: BEETLE PROBLEM A study is conducted to…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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BEETLE PROBLEM
A study is conducted to determine the height of a beetle which is distinctively
different among other insects. The researcher randomly selected 25 insects. Each
insect was classified as either a beetle or other and the height (in inches) was
measured. The data was recorded in "beetle_ex6.xlsx" inside the "beetle" tab.
R Software output and Confusion Matrix:
> Logit Model Summary
Coefficients:
a.
b.
Estimate Std. Error z value Pr(>lzl)
(Intercept) -6.41906 6.18612 -1.038 0.299
Height
0.316
0.08949
0.08927 1.002
> Wald's Test
Model 1: Insect
Model 2: Insect 1
P
Height
#Df LogLik Df Chisq Pr>Chisq)
1 2 -16.624
2
1 17.148 -1 1.0483
0 (Other)
1 (Beetle)
Total
> Confusion Matrix
Insect (True
value)
Predicted
Probability
T≤0.5
(0)
10
7
17
0.3059
T>0.5
(1)
4
4
8
Total
14
11
25
Construct the logistic regression model both in terms of probability and log odds.
Interpret the coefficient of the model constructed in terms of odds.
Calculate the sensitivity, specificity and %accuracy of the model (# of correctly
predicted/number of samples *100)
NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis
in words, test procedure, p-value, decision, & conclusion. Use α=0.05

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Follow-up question about the beetle problem above,

After (a) constructing the logistic regression model both in terms of probability and log odds, and (b) interpreting the coefficient of the model constructed in terms of odds, and (c) calculating the sensitivity, specificity and % accuracy of the model (# of correctly predicted/number of samples *100),

Assess the fit of the model using Wald’s test at 5% level of significance (Include Ho, Ha, p-value and conclusion); and
What is the probability that the insect is a beetle given that the height is 75 inches?

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