Week 6 Exam

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Apr 3, 2024

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Statistical Models Exam 93% 1. Based on the linear regression, how much would you expect a 0.55 carat diamond to cost? $1,800 $2,100 $2,500 $2,900 2. Based on the linear regression, how much would you expect a diamond that costs $5,500 to weigh?

0.72 carats 0.78 carats 0.81 carats 0.90 carats 3. You're surprised to learn that instead of ~$100, a 0.30 carat costs ~$800 carats. Which explanation would make sense? The linear regression is not accurate at predicting the cost of diamonds below 0.40 carats. There is a fixed cost associated with procuring the diamond and offering it for sale, meaning that small diamonds have a relatively high price. The diamond is very high quality as measured by other metrics (e.g., cut, clarity, color). All of the above. 4. If a residual is negative, what does it mean about the observed value? The predicted value is greater than the observed value. The predicted value is equal to the observed value. The predicted value is less than the observed value. It cannot be determined from the data provided. 5.

If the expected value of a diamond is $3,500, but the observed value is $3,800, what is the residual? -$600 -$300 $300 $600 6. Which of the datasets has the strongest correlation between the variable on the x-axis and the variable on the y-axis? Weight to Miles per Gallon Horsepower to Miles per Gallon Horsepower to Time from 0-60 mph It cannot be determined from the data provided. 7. Which of the correlation coefficients indicates the weakest correlation between the variables? r = -0.88 r = - 0.52 r = 0.05 r = 0.83 8. If the correlation between the price of two stocks is 0.83, what does this indicate? No correlation Weak positive correlation Moderate positive correlation Strong positive correlation 9. If the image represents the relationship between the weight of a diamond and its price, how would you interpret the regression models?

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Both the linear and nonlinear models predict well, but the linear model is slightly better. Both the linear and nonlinear models predict well, but the nonlinear model is slightly better. Neither model would be good to use to predict the price of diamonds. More information is needed to answer this question. 10. If the coefficient of determination between the price of a house and it square footage is 65%, what percentage of the variation in the price of the house is explained by its size? 0% 35% 65% 81% View answer 11. If the correlation coefficient between the price of a car and its mileage is 60%, what percentage of the price of the car is explained by its mileage? 36% 40% 60% 80%

12. If the regression line comparing the age of a used car to its price has the equation c = - 3000a + 36000, what is the expected cost of an 8-year-old car? $0 $6,000 $9,000 $12,000 13. If the regression line comparing the age of a used car to its price has the equation c = - 3000a + 36000 and the residual is $3,000, what is the observed cost of an 8-year-old car? $0 $3,000 $9,000 $15,000 14. If the regression line comparing the age of a used car to its price has the equation c = - 3000a + 36000, what is the expected age of a car that costs $27,000? 2 years 3 years 8 years 12 years 15. If the r-squared of the regression line comparing the age of a used motorcycle to its cost is 64%, what is the correlation coefficient? -0.80 -0.64 0.0 0.36 0.64

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