Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Answer Coefficients 1278 230.04 Coefficients Does the sign of the coefficient for the variable safety rating make sense? -140.58 328.63 Standard Error 129.86 23.23 14.97 397.29 t Stat 9.841 P-value 0.0000 9.903 0.0000 -9.391 0.0000 0.827 0.4117 O No, because it is expected that as the safety rating increases then the cost should decrease. O Yes, because it is expected that as the safety rating increases then the cost should decrease. O No, because it is expected that as the safety rating increases then the cost should also increase. O Yes, because it is expected that as the safety rating increases then the cost should also increase. Tables Keypad Keyboard Shortcuts

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**Understanding Multiple Regression Analysis: Car Insurance Cost**

Consider the following analysis output from a multiple regression model. This model relates the cost of car insurance to variables such as the number of car accidents, driver's credit score, and the safety rating of the car.

| **Coefficients**       | **Coefficients** | **Standard Error** | **t Stat** | **P-value** |
|------------------------|------------------|--------------------|------------|-------------|
| **Intercept**          | 1278             | 129.86             | 9.841      | 0.0000      |
| **Car Accidents (In last 3 years)** | 230.04           | 23.23              | 9.903      | 0.0000      |
| **Credit Score**       | -140.58          | 14.97              | -9.391     | 0.0000      |
| **Safety Rating**      | 328.63           | 397.29             | 0.827      | 0.4117      |

**Analysis:**

- **Intercept (1278):** Represents the base cost of car insurance without considering other variables.
- **Car Accidents (230.04):** A positive coefficient indicates that more accidents increase insurance costs, with a statistically significant P-value of 0.0000.
- **Credit Score (-140.58):** A negative coefficient suggests higher credit scores decrease costs, also highly significant statistically.
- **Safety Rating (328.63):** Although the coefficient is positive, the high P-value (0.4117) implies it is not statistically significant, which questions its impact on cost.

**Question:**

Does the sign of the coefficient for the variable safety rating make sense?

**Answer Options:**

- ○ No, because it is expected that as the safety rating increases then the cost should decrease.
- ○ Yes, because it is expected that as the safety rating increases then the cost should decrease.
- ○ No, because it is expected that as the safety rating increases then the cost should also increase.
- ○ Yes, because it is expected that as the safety rating increases then the cost should also increase.
Transcribed Image Text:**Understanding Multiple Regression Analysis: Car Insurance Cost** Consider the following analysis output from a multiple regression model. This model relates the cost of car insurance to variables such as the number of car accidents, driver's credit score, and the safety rating of the car. | **Coefficients** | **Coefficients** | **Standard Error** | **t Stat** | **P-value** | |------------------------|------------------|--------------------|------------|-------------| | **Intercept** | 1278 | 129.86 | 9.841 | 0.0000 | | **Car Accidents (In last 3 years)** | 230.04 | 23.23 | 9.903 | 0.0000 | | **Credit Score** | -140.58 | 14.97 | -9.391 | 0.0000 | | **Safety Rating** | 328.63 | 397.29 | 0.827 | 0.4117 | **Analysis:** - **Intercept (1278):** Represents the base cost of car insurance without considering other variables. - **Car Accidents (230.04):** A positive coefficient indicates that more accidents increase insurance costs, with a statistically significant P-value of 0.0000. - **Credit Score (-140.58):** A negative coefficient suggests higher credit scores decrease costs, also highly significant statistically. - **Safety Rating (328.63):** Although the coefficient is positive, the high P-value (0.4117) implies it is not statistically significant, which questions its impact on cost. **Question:** Does the sign of the coefficient for the variable safety rating make sense? **Answer Options:** - ○ No, because it is expected that as the safety rating increases then the cost should decrease. - ○ Yes, because it is expected that as the safety rating increases then the cost should decrease. - ○ No, because it is expected that as the safety rating increases then the cost should also increase. - ○ Yes, because it is expected that as the safety rating increases then the cost should also increase.
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