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EBK FINITE MATHEMATICS FOR THE MANAGERI
- Consider the following data points. P₁(1, 8), P₂(2, 6), Ps(5, 6), P4(6, 5), Ps(10, 1) (a) Find the equation of the least-squares line for the data. (Round all coefficients to two decimal places.) y (b) Draw a scatter diagram for the data and graph the least-squares line. y 8 6 2 6 2 8 8 10 10 2 4 2 2 8 8 10 10 xarrow_forwardIt is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 2 5 6 y 48 41 33 26 Find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.) = + xarrow_forwardLeast squares II Consider the four points (200,1950),(400,1650), (600,1800), and (800,1600). The leastsquares line is yn = 1975 - 0.45x. Explain what “leastsquares” means, using these data as a specific example.arrow_forward
- The symbol for the intercept of a least squares line is O A. b, О В. г OC. Sy O D. y O E. boarrow_forwardа. Complete the table. (or just write answers) Xi Yi 2 2 3 4 Totals E x; = E yi = Exf = Σχy Find SSxy, SSXX B1. x, y, and fo- Write the equation of the least squares line. b. C. d) What will be y if x=10arrow_forwardIn any scatterplot, ordinary least squares (OLS) regression finds: the intersection of two lines that produce the smallest sum of squares. one line that produces the largest sum of squares. the intersection of two lines that produces the largest sum of squares. one line that produces the smallest sum of squares.arrow_forward
- 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?arrow_forwardThe 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 27arrow_forwardPercentages of public school students in fourth grade in 1996 and in eighth grade in 2000 who were at or above the proficient level in mathematics are given for eight western states. Find the equation of the least-squares line that summarizes the relationship between x = 1996 fourth-grade math proficiency percentage and y = 2000 eighth-grade math proficiency percentage. (Give the numerical values to four decimal places.) |4th grade 8th grade (1996) State (2000) Arizona 15 21 California 11 18 Hawaii 16 16 Montana 22 37 New Mexico 13 13 Oregon 21 32 Utah 23 26 Wyoming 19 25 n USE SALT ŷ =arrow_forward
- You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). 2 3 12 16 26 150 36 y | 45 48 70 100 200 A USE SALT Complete parts (a) through (e), given Ex = 95, Ey = 613, Ex² 2385, Σy2 %3D = 81,729, Exy = 13,774, and r - 0.9918. (a) Draw a scatter diagram displaying the data. 210 Graph Layers 200 190 After you add an object to the graph you 180 can use Graph Layers to view and edit its 170 properties. 160 Fill 150 140 130 120 110 100 No Solution 90 80 70 60 50 40 +30 O Help 20 25 30 35 10 15 40 WebAssign. Graphing Tool (b) Verify the given sums Ex, Ey, Ex², Ey², Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex = Ey = Ex² = Ey? = Exy = (c) Find x, and y. Then find the equation of the least-squares…arrow_forwardThe following table gives retail values of a 2017 Corvette for various odometer readings. (a) Find the equation of the least-squares line for the data. (Where odometer reading is the independent variable, x, and retail value is the dependent variable. Round your numerical values to two decimal places.) (b) Use the equation from part (a) to predict the retail price of a 2017 Corvette with an odometer reading of 30,000. Round to the nearest $100. (c) Find the linear correlation coefficient for these data. (Round your answer to four decimal places.)arrow_forwardThe 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 1077.0arrow_forward
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