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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 Coefficients 1186 213.48 Coefficients - 130.46 294.11 Standard Error t Stat 9.575 Does the sign of the coefficient for the variable safety rating make sense? 123.87 21.89 14.26 356.37 P-value 0.0000 9.752 0.0000 -9.149 0.825 0.0000 0.4128

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 Coefficients 1186 213.48 Coefficients - 130.46 294.11 Standard Error t Stat 9.575 Does the sign of the coefficient for the variable safety rating make sense? 123.87 21.89 14.26 356.37 P-value 0.0000 9.752 0.0000 -9.149 0.825 0.0000 0.4128

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.6: Regression And Median-fit Lines
Problem 6PPS
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Sure! Here's the transcription of the text from the image: --- 1. ☐ Yes, because it is expected that as the *safety rating* increases then the *cost* should decrease. 2. ☐ No, because it is expected that as the *safety rating* increases then the *cost* should also increase. 3. ☐ Yes, because it is expected that as the *safety rating* increases then the *cost* should also increase. 4. ☐ No, because it is expected that as the *safety rating* increases then the *cost* should decrease. --- There are no graphs or diagrams present in the image.
Transcribed Image Text:Sure! Here's the transcription of the text from the image: --- 1. ☐ Yes, because it is expected that as the *safety rating* increases then the *cost* should decrease. 2. ☐ No, because it is expected that as the *safety rating* increases then the *cost* should also increase. 3. ☐ Yes, because it is expected that as the *safety rating* increases then the *cost* should also increase. 4. ☐ No, because it is expected that as the *safety rating* increases then the *cost* should decrease. --- There are no graphs or diagrams present in the image.
**Transcription: Educational Context** 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. | Coefficients | Coefficients | Standard Error | t Stat | P-value | |------------------|--------------|----------------|--------|---------| | Intercept | 1186 | 123.87 | 9.575 | 0.0000 | | Car Accidents (In last 3 years) | 213.48 | 21.89 | 9.752 | 0.0000 | | Credit Score | -130.46 | 14.26 | -9.149 | 0.0000 | | Safety Rating | 294.11 | 356.37 | 0.825 | 0.4128 | **Explanation of Coefficients Table:** - **Intercept**: The baseline cost of insurance is represented by the intercept, which is 1186. This is the estimated cost when all other variables are zero. - **Car Accidents**: For each additional car accident in the last three years, the cost of insurance increases by 213.48. The small P-value (0.0000) indicates this is a statistically significant predictor. - **Credit Score**: A higher credit score is associated with a decrease in insurance costs, as shown by the coefficient of -130.46. This predictor is statistically significant with a P-value of 0.0000. - **Safety Rating**: While a higher safety rating shows an increase in cost by 294.11, this factor is not statistically significant given the P-value of 0.4128. **Question for Learners:** Does the sign of the coefficient for the variable safety rating make sense? Reflect on why a higher safety rating might not be expected to increase costs and whether this result could be due to statistical variance or model specification issues.
Transcribed Image Text:**Transcription: Educational Context** 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. | Coefficients | Coefficients | Standard Error | t Stat | P-value | |------------------|--------------|----------------|--------|---------| | Intercept | 1186 | 123.87 | 9.575 | 0.0000 | | Car Accidents (In last 3 years) | 213.48 | 21.89 | 9.752 | 0.0000 | | Credit Score | -130.46 | 14.26 | -9.149 | 0.0000 | | Safety Rating | 294.11 | 356.37 | 0.825 | 0.4128 | **Explanation of Coefficients Table:** - **Intercept**: The baseline cost of insurance is represented by the intercept, which is 1186. This is the estimated cost when all other variables are zero. - **Car Accidents**: For each additional car accident in the last three years, the cost of insurance increases by 213.48. The small P-value (0.0000) indicates this is a statistically significant predictor. - **Credit Score**: A higher credit score is associated with a decrease in insurance costs, as shown by the coefficient of -130.46. This predictor is statistically significant with a P-value of 0.0000. - **Safety Rating**: While a higher safety rating shows an increase in cost by 294.11, this factor is not statistically significant given the P-value of 0.4128. **Question for Learners:** Does the sign of the coefficient for the variable safety rating make sense? Reflect on why a higher safety rating might not be expected to increase costs and whether this result could be due to statistical variance or model specification issues.
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