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)

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**Part 2: Prediction Models and Change Analysis**

---

**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).

---

**Model Equation:**

\[ Y = 2.7 + 0.94 (\ln X) \]

---

**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 |
| ------- | ---------- | ---------- | ---- | -------------------------------- | ----------------------------------------------- | 
|         |            |            |      |                                  |                                                 | 

---

**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 \( X \).

---

This structured approach will help in understanding the behavior of the given model and the sensitivity
Transcribed Image Text:**Part 2: Prediction Models and Change Analysis** --- **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). --- **Model Equation:** \[ Y = 2.7 + 0.94 (\ln X) \] --- **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 | | ------- | ---------- | ---------- | ---- | -------------------------------- | ----------------------------------------------- | | | | | | | | --- **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 \( X \). --- This structured approach will help in understanding the behavior of the given model and the sensitivity
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