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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: Estimate Std. Error z value Pr(>lzl) (Intercept) -6.41906 6.18612 -1.038 0.299 Height 0.08927 1.002 0.316 0.08949 > Wald's Test Model 1: Insect ~ Height Model 2: Insect ~ 1 #Df LogLik Df Chisq Pr(>Chisq) 1 2 -16.624 2 1 -17.148 -1 1.0483 > Confusion Matrix Insect (True value) 0 (Other) 1 (Beetle) Total 0.3059 Predicted Probability T≤0.5 (0) 10 7 17 T>0.5 (1) 4 4 8 Total 14 11 25 a. Construct the logistic regression model both in terms of probability and log odds. b. Interpret the coefficient of the model constructed in terms of odds. c. Calculate the sensitivity, specificity and accuracy of the model (# of correctly predicted/number of samples *100) d. Assess the fit of the model using Wald's test at 5% level of significance (Include Ho, Ha, p-value and conclusion) e. What is the probability that the insect is a beetle given that the height is 75 inches? NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis in words, test procedure, p-value, decision, & conclusion. Use α=0.05

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: Estimate Std. Error z value Pr(>lzl) (Intercept) -6.41906 6.18612 -1.038 0.299 Height 0.08927 1.002 0.316 0.08949 > Wald's Test Model 1: Insect ~ Height Model 2: Insect ~ 1 #Df LogLik Df Chisq Pr(>Chisq) 1 2 -16.624 2 1 -17.148 -1 1.0483 > Confusion Matrix Insect (True value) 0 (Other) 1 (Beetle) Total 0.3059 Predicted Probability T≤0.5 (0) 10 7 17 T>0.5 (1) 4 4 8 Total 14 11 25 a. Construct the logistic regression model both in terms of probability and log odds. b. Interpret the coefficient of the model constructed in terms of odds. c. Calculate the sensitivity, specificity and accuracy of the model (# of correctly predicted/number of samples *100) d. Assess the fit of the model using Wald's test at 5% level of significance (Include Ho, Ha, p-value and conclusion) e. What is the probability that the insect is a beetle given that the height is 75 inches? NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis in words, test procedure, p-value, decision, & conclusion. Use α=0.05

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 75E
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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: Estimate Std. Error z value Pr(>lzl) (Intercept) -6.41906 6.18612 -1.038 0.299 Height 0.08927 1.002 0.08949 0.316 > Wald's Test Model 1: Insect Height Model 2: Insect 1 #Df LogLik Df Chisq Pr(>Chisq) 1 2 -16.624 2 1 -17.148 -1 1.0483 > Confusion Matrix Insect (True value) 0 (Other) 1 (Beetle) Total 0.3059 Predicted Probability π<0.5 (0) 10 7 17 T>0.5 (1) 4 4 8 Total 14 11 25 a. Construct the logistic regression model both in terms of probability and log odds. b. Interpret the coefficient of the model constructed in terms of odds. c. Calculate the sensitivity, specificity and %accuracy of the model (# of correctly predicted/number of samples *100) d. Assess the fit of the model using Wald's test at 5% level of significance (Include Ho, Ha, p-value and conclusion) e. What is the probability that the insect is a beetle given that the height is 75 inches? NOTE: For items requiring test of hypotheses, specify the null & alternative hypothesis in words, test procedure, p-value, decision, & conclusion. Use α=0.05
Transcribed Image Text: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: Estimate Std. Error z value Pr(>lzl) (Intercept) -6.41906 6.18612 -1.038 0.299 Height 0.08927 1.002 0.08949 0.316 > Wald's Test Model 1: Insect Height Model 2: Insect 1 #Df LogLik Df Chisq Pr(>Chisq) 1 2 -16.624 2 1 -17.148 -1 1.0483 > Confusion Matrix Insect (True value) 0 (Other) 1 (Beetle) Total 0.3059 Predicted Probability π<0.5 (0) 10 7 17 T>0.5 (1) 4 4 8 Total 14 11 25 a. Construct the logistic regression model both in terms of probability and log odds. b. Interpret the coefficient of the model constructed in terms of odds. c. Calculate the sensitivity, specificity and %accuracy of the model (# of correctly predicted/number of samples *100) d. Assess the fit of the model using Wald's test at 5% level of significance (Include Ho, Ha, p-value and conclusion) e. What is the probability that the insect is a beetle given that the height is 75 inches? 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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1.. Assess the fit of the model using Wald's test at 5% level of significance (Include Ho, Ha, p-value and conclusion)

2. What is the probability that the insect is a beetle given that the height is 75 inches?

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Assess the fit of the model using Wald’s test at 5% level of significance (Include Ho, Ha, p-value and conclusion)

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