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(>Izl) (Intercept) -6.41906 6.18612 -1.038 Height 0.08927 1.002 0.08949 > Wald's Test Model 1: Insect Model 2: Insect ~ 1 1 2 N Height #Df LogLik Df Chisq Pr(>Chisq) 2 -16.624 1 -17.148 -1 1.0483 0 (Other) 1 (Beetle) Total > Confusion Matrix Insect (True value) Predicted Probability π<0.5 (0) 10 7 17 0.3059 T>0.5 (1) 4 4 8 Total 14 11 25 0.299 0.316 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
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(>Izl) (Intercept) -6.41906 6.18612 -1.038 Height 0.08927 1.002 0.08949 > Wald's Test Model 1: Insect Model 2: Insect ~ 1 1 2 N Height #Df LogLik Df Chisq Pr(>Chisq) 2 -16.624 1 -17.148 -1 1.0483 0 (Other) 1 (Beetle) Total > Confusion Matrix Insect (True value) Predicted Probability π<0.5 (0) 10 7 17 0.3059 T>0.5 (1) 4 4 8 Total 14 11 25 0.299 0.316 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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 35EQ
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Transcribed Image Text: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
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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