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- Each month for several months, the average temperature in °C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.11x. a) Predict the number of pounds of steam consumed in a month where the average temperature is 65°C. Round the answer to two decimal places. b) If two months differ in their average temperatures by 5°C, by how much do you predict the number of pounds of steam consumed to differ? Round the answer to two decimal places.The accompanying data resulted from an experiment in which weld diameter x and shear strength y (in pounds) were determined for five different spot welds on steel. A scatterplot shows a pronounced linear pattern. The least-squares line is = -964.98 + 8.60x. Because 1 lb = 0.4536 kg, strength observations can be re-expressed in kilograms through multiplication by this conversion factor: new y = 0.4536(old y). What is the equation of the least-squares line when y is expressed in kilograms? (Give the answer to two decimal places.) = x 202.9 212.9 222.9 232.9 242.8 y 814.5 786.1 961.2 1118.8 1077.0Select the equation of the least squares line for the data: (51.00, 1.0), (48.75, 2.5), (52.50, .5), (46.50, 5.0), (45.00, 4.5), (41.25, 6.5), (43.50, 5.0). a) ŷ = -28.956 − 0.54067x b) ŷ = 28.956 − 0.59474x c) ŷ = 0.54067x − 28.956 d) ŷ = 31.852 − 0.59474x e) ŷ = 28.956 − 0.54067x f) None of the above
- Each month for several months, the average temperature in °C (x) and the number of pounds of steam (y) consumed by a certain chemical plant were measured. The least-squares line computed from the resulting data is y = 245.82 + 1.13x. Predict the number of pounds of steam consumed in a month where the average temperature is 65°C. If two months differ in their average temperatures by 5°C, by how much do you predict the number of pounds of steam consumed to differ?A lab received a new instrument to measure pH. To compare the new instrument to the old lab instrument, 11 samples were measured with both pieces of equipment. Using the data (below), find the least squares equation (x = "pH old" and Y = "pH new") and then predict the value on the new instrument if the old instrument gave a pH of 6.30. Enter your answer using 3 significant digits. pH Old pH New 6.35 6.16 6.01 5.95 6.15 6.05 6 6.01 6.11 6.06 5.93 5.83 5.84 5.81 5.63 5.71 5.63 5.74 6.11 6.1 6.07 6.01In a study of the relationship between the Brinell hardness (x) and tensile strength in ksi (y) of specimens of cold drawn copper, the least-squares line was y = −196.32 + 2.42x. Predict the tensile strength of a specimen whose Brinell hardness is 102.7. If two specimens differ in their Brinell hardness by 3, by how much do you predict their tensile strengths to differ?
- The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. Weight |(pounds), x Miles per Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27In the manufacture of synthetic fiber, the fiber is often “set” by subjecting it to high temperatures. The object is to improve the shrinkage properties of the fiber. In a test of 23 yarn specimens, the relationship between temperature in °C (x) and shrinkage in % (y) was summarized by the least-squares line y = −12.789 + 0.133x. The total sum of square was ∑ni=1(yi−y⎯⎯)2∑i=1n(yi−y¯)2 = 57.313, and the estimated error variance was s2 = 0.0670. Compute the coefficient of determination r 2. Round the answer to three decimal places.The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x+ 41.337. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Click the icon to view the data table. Data Table ..... Weight (pounds), x Miles per (a) The coefficient of determination of the expanded data set is R = %. Gallon, y (Round to one decimal place as needed.) Car 1 3,771 22 Car 2 ,990 19 Car 3 3,534 20 Car 4 3,172 24 Car 5 2,579 27 Car 6 3,730 20 Car 7 2,605 25 Car 8 3,777 19 Car 9 3,308 19 Car 10 2,997 26 Car 11 2,751 27
- The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. ..... (a) The coefficient of determination of the expanded data set is R = %. Weight (pounds), x Miles per (Round to one decimal place as needed.) Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27please solve quicklyWhen the predicted overnight temperature is between 15°F and 32°F, roads in northern cities are salted to keep water from freezing on the roadways. Suppose that a small city was trying to determine the average amount of salt y (in tons) needed per night at temperature x. They found the following least squares prediction equation: y = 20,000 - 2,500x Interpet the slope. a) 2,500 tons is the decrease in the amount of salt needed for a 1 degree increase in temperature. b) 2,500 tons is the increase in the amount of salt needed for a 1 degree increase in temperature. c) 20,000 is the increase in the amount of salt needed for a 1 degree increase in temperature. d) 2,500 tons is the expected amount of salt needed when the temperatures is 0° C.