14. John's parents recorded his height at various ages between 36 and 66 months. Below is a record of the results: 60 66 43 45 Age (months) Height (inches) 36 34 48 54 38 41 Which of the following is the equation of the least-squares regression line of John's height on age? (Note: You do not need to directly calculate the least-squares regression line to answer this qu O Height = 12 x (Age) O Height = Age/12 O Height = 60 - 0.22 x (Age) O Height = 22.3 + 0.34 x (Age) 15. A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their curre beginning salary is = -2532.7 + 2.12x. Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Mrs. Jones? O $1187.30 O $2252.70 O $2812.70 O Cannot be determined from the information given. 16. Which of the following statements about least-squares regression involving two quantitative variables, x and y, is/are TRUE? O A change of one standard deviation in x corresponds to a change of r standard deviations in y. O The least-squares regression line always passes through the point ( ). O The square of the correlation, , is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x. O The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.
14. John's parents recorded his height at various ages between 36 and 66 months. Below is a record of the results: 60 66 43 45 Age (months) Height (inches) 36 34 48 54 38 41 Which of the following is the equation of the least-squares regression line of John's height on age? (Note: You do not need to directly calculate the least-squares regression line to answer this qu O Height = 12 x (Age) O Height = Age/12 O Height = 60 - 0.22 x (Age) O Height = 22.3 + 0.34 x (Age) 15. A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their curre beginning salary is = -2532.7 + 2.12x. Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Mrs. Jones? O $1187.30 O $2252.70 O $2812.70 O Cannot be determined from the information given. 16. Which of the following statements about least-squares regression involving two quantitative variables, x and y, is/are TRUE? O A change of one standard deviation in x corresponds to a change of r standard deviations in y. O The least-squares regression line always passes through the point ( ). O The square of the correlation, , is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x. O The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.
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Can you please help me with questions 14-16? Thank you!
Transcribed Image Text:14. John's parents recorded his height at various ages between 36 and 66 months. Below is a record of the results:
Age (months)
Height (inches)
36
48
54
34
38
60 66
45
41
43
Which of the following is the equation of the least-squares regression line of John's height on age? (Note: You do not need to directly calculate the least-squares regression line to answer this question.)
O Height = 12 x (Age)
O Height = Age/12
O Height = 60 - 0.22 x (Age)
O Height = 22.3 + 0.34 x (Age)
15. A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their
beginning salary is = -2532.7 + 2.12x.
Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Mrs. Jones?
O $1187.30
O $2252.70
O $2812.70
O Cannot be determined from the information given.
16. Which of the following statements about least-squares regression involving two quantitative variables, x and y, is/are TRUE?
O A change of one standard deviation in x corresponds to a change of r standard deviations in y.
O The least-squares regression line always passes through the point (.).
O The square of the correlation, , is the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.
O The least-squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.
O All of these answers are true.
17. A researcher wishes to determine whether the rate of water flow (in liters per second) over an experimental soil bed can be used to predict the amount of soil washed away (in kilograms). The researcher measures the
amount of soil washed away for various flow rates, and from these data calculates the least-squares regression line to be
Amount of eroded soil = 0.4 + 1.3 x (flow rate)
What do we know about the correlation between amount of eroded soil and flow rate?
Or= 1/1.3
Or= 0.4
Submit
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