Part 2. For each of the following models, state what the expected value of Y is when X = 50. Also, state how the predicted value of Y changes when X increases by 5, units (i.e., a 10% increase). Problem X=50 X=55 Diff 5 Units increase in X causes Y to 10% change in X causes the following % change in Y Y= 2.7+0.94(InX)
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![**Part 2: Prediction Models and Change Analysis**
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**Instructions:**
For each of the following models, state what the expected value of \( Y \) is when \( X = 50 \). Also, state how the predicted value of \( Y \) changes when \( X \) increases by 5 units (i.e., a 10% increase).
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**Model Equation:**
\[ Y = 2.7 + 0.94 (\ln X) \]
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**Table Layout:**
| Problem | \( X = 50 \) | \( X = 55 \) | Diff | 5 Units increase in X causes Y to | 10% change in X causes the following % change in Y |
| ------- | ---------- | ---------- | ---- | -------------------------------- | ----------------------------------------------- |
| | | | | | |
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**Explanation of the Table:**
- **Columns:**
- **Problem:** Refers to the specific prediction model or problem being analyzed.
- **\( X = 50 \):** The value of \( Y \) when \( X \) is 50.
- **\( X = 55 \):** The value of \( Y \) when \( X \) is 55.
- **Diff:** The difference in the value of \( Y \) between \( X = 50 \) and \( X = 55 \).
- **5 Units increase in X causes Y to:** Describes the change in \( Y \) when \( X \) increases by 5 units.
- **10% change in X causes the following % change in Y:** Describes the percentage change in \( Y \) when \( X \) increases by 10%.
**Analysis Workflow:**
1. **Calculate the values of \( Y \) for \( X = 50 \) and \( X = 55 \)** using the given model equation.
2. **Determine the difference (Diff)** between the values of \( Y \) at \( X = 50 \) and \( X = 55 \).
3. **Analyze the effect of a 5-unit increase in \( X \)** on the value of \( Y \).
4. **Evaluate the percentage change** in \( Y \) corresponding to a 10% increase in \( X \).
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This structured approach will help in understanding the behavior of the given model and the sensitivity](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc13bfa47-d8b1-49a8-8652-3d3d8ccb6fe9%2Ff6c8d874-0451-45ac-b9c1-7555dbdacd56%2Fwwssatu_processed.png&w=3840&q=75)
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