Question

14. Multiple Choice Variables x and y have a correlation coefficient of r = 0.89. Which statement is best? a. There is a strong positive association between x and y and a straight line fit to the data cannot be substantially improved by fitting a curve to the data. b. There is a strong positive association between x and y and a straight line fit to the data can certainly be substantially improved by fitting a curve to the data. c. There is a strong positive association between x and y, but we do not have enough information to determine whether or not a straight line fit to the data could be substantially improved by fitting a curve to the data. d. There is neither a strong linear nor non-linear relationship between x and y. 15. Multiple Choice The growth of a boy is estimated from measurements of height taken every six months from age 2 years to 12 years. The correlation coefficient is r = 0.997 and a residual plot shows no patterns and an excellent fit of a straight line. The fitted model is: y = 30 + 0.25x where x is age in months and ŷ is the fitted height in inches. Which statement is best? a. The intercept of 30 inches is a good estimate of the height of the boy at birth (age x equal to zero months). b. The intercept of 30 inches may not be a good estimate of the height of the boy at birth because of a lack of independence of the measurements. c. The intercept of 30 inches may not be a good estimate of the height of the boy at birth because of nonconstant variance. d. The intercept of 30 inches may not be a good estimate of the height of the boy at birth because of extrapolation.

Answer 1

14. Multiple Choice Variables x and y have a correlation coefficient of r = 0.89. Which statement is best? a. There is a strong positive association between x and y and a straight line fit to the data cannot be substantially improved by fitting a curve to the data. b. There is a strong positive association between x and y and a straight line fit to the data can certainly be substantially improved by fitting a curve to the data. There is a strong positive association between x and y, but we do not have enough information to determine whether or not a straight line fit to the data could be substantially improved by fitting a curve to the data d. There is neither a strong linear nor non-linear relationship between x and y. 15. Multiple Choice The growth of a boy is estimated from measurements of height taken every six months from age 2 years to 12 years. The correlation coefficient is r = 0.997 and a residual plot shows no patterns and an excellent fit of a straight line. The fitted model is: y = 30 + 0.25x where x is age in months and ŷ is the fitted height in inches. Which statement is best? a. The intercept of 30 inches is a good estimate of the height of the boy at birth (age x equal to zero months). de intercept of 30 inches may not be a good estimate of the height of the boy at birth because of a lack of independence of the measurements. c. The intercept of 30 inches may not be a good estimate of the height of the boy at birth because of nonconstant variance. d. The intercept of 30 inches may not be a good estimate of the height of the boy at birth because of extrapolation.

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