A paper company has about 50 paper mills distributed over 3 provinces. Each mill records specified factors that contribute to its profitability. The company has classified the mills as Profitable and Non- Profitable. They recorded paper weight produced as an indicator of profitability. That is, X₁ = PAPER (weight in 10000 kilograms) Y = PROF (1 = profitable and 0 = not profitable) Y Profitable 1 1 Paper 2 1.5

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
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Chapter11: Data Analysis And Probability
Section11.2: Box-and-whisker Plots
Problem 2E
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A paper company has about 50 paper mills distributed over 3 provinces. Each mill records specified
factors that contribute to its profitability. The company has classified the mills as Profitable and Non-
Profitable. They recorded paper weight produced as an indicator of profitability. That is,
X₁ = PAPER (weight in 10000 kilograms)
Y = PROF (1 = profitable and 0 = not profitable)
Y Profitable
1
1
0
It was found that
Paper
2
1.5
0.8
ît=
exp(-2.94 + 0.098X₁)
1 + exp(-2.94 +0.098X₁)
1. Give the fitted logistic response function.
2. Give the fitted logit response function
3. Show that
ft
loge € (₁^²) = = -2.94 + 0.098X₁
4. Give the odds to be used of this logistic regression for X₁ = 0.7. Explain your result.
5. What is the estimated probability that a mill be profitable if it produces 7 000 kilograms of paper?
7. Interpret the regression coefficients of
ît=
Also find the odds ratio for b₁.
exp(-2.94 + 0.098X₁)
1 + exp(-2.94 +0.098X₁)
Transcribed Image Text:A paper company has about 50 paper mills distributed over 3 provinces. Each mill records specified factors that contribute to its profitability. The company has classified the mills as Profitable and Non- Profitable. They recorded paper weight produced as an indicator of profitability. That is, X₁ = PAPER (weight in 10000 kilograms) Y = PROF (1 = profitable and 0 = not profitable) Y Profitable 1 1 0 It was found that Paper 2 1.5 0.8 ît= exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁) 1. Give the fitted logistic response function. 2. Give the fitted logit response function 3. Show that ft loge € (₁^²) = = -2.94 + 0.098X₁ 4. Give the odds to be used of this logistic regression for X₁ = 0.7. Explain your result. 5. What is the estimated probability that a mill be profitable if it produces 7 000 kilograms of paper? 7. Interpret the regression coefficients of ît= Also find the odds ratio for b₁. exp(-2.94 + 0.098X₁) 1 + exp(-2.94 +0.098X₁)
Expert Solution
Step 1

From the given information, y is the predicted variable and x is the predictor variable.

The general logistic curve is of the form

π^=eβo+β1x11+eβo+β1x1 ----------(I)

Here, βo is the intercept and β1 is the slope

 

 

 

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