Q #1

4. [0.82/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.008.5. You are the foreman of the Bar- 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). LOL USE SALT Complete parts (2) through (c). given Ex - 89, Ey - 610, Ex - 2297, Dy- 81,626, Exy - 13,417, and r - 0.9982. (2) Draw a scatter diagram displaying the data 35 200 150 yical weight in kilograms ) yocalf weight (in kilograms) 100 100 150 10 15 20 25 30 35 O x (age of calf (in weeks)) x (age of calf (in weeks)) y (call weight (In kilograms)) 100 150 200 O x (age of calf (in weeks)) 200 150 y (calf weight (in kilograms)) 100 10 15 20 25 30 x (age of calf (in weeks)) (b) Verify the given sums Ex, Ly, Ex, Ly'd, Exy, and the value of the sample correlation cooff it . (Round your value for r to four decimal places.) Ex - 89 Ey - 610 2x- 13417 (XXX Exp - 816265. [0.76/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.010.5. It 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 (Le., over and above) the opposing team. Let y be the percentage of time number of fouls wins the game 49 42 LA USE SALT Complete parts (a) through (e), given Ex - 16, Ey - 150, Ex - 78, zy - 5930, Exy - 538, and r - -0.9489. (2) Draw a scatter diagram displaying the data. 50 45 y (percentage) y(percentagej y (percentage y (percentage) 35 35 40 45 35 45 x ( fouls) C x ( fouls) x ( fouls) x ( fouls) (b) Verify the given sums Ex, Ly, Ex , Ty , Exy, and the value of the efficient r. (Round your value for r to four decimal places.) Ex - 16 Ey - 150 2x- 638 EV - 78 Exy - 5930 1x - -0.9488 (c) Find x, and y. Then find the equation of the least overs to four decimal places.) x - 4.0800 - 65 2143 + 4.4286 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. 30 45 y (percentage) y (percentage) y (percentage) y (percentage) 35 w 30 35 40 45 35 45 x ( fouls) x (fouls) x ( fouls) x (fouls) (e) Find the value of the coefficient of deter an r. What perc ation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for I to four decimal places. Round your arewers for the percentages to two decimal place.) 2 0.9002 explained 90 02 unexplained6. [0.82/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.012.5. Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5%% of all fatal accidents of 37-year-olds are due to fallure to yield the right of way. 47 57 10 17 31 87 LA USE SALT Complete parts (a) through (e). given Ex - 372, By - 112, Ex- - 24814, Ey2 - 3120, Ixy - 8224, and / = 0.9537. (a] Draw a scatter diagram displaying the data. 08 80 TO y (percentage of all fatal accidents) y (percentage of all fatal accidents) y (percentage of all fatal accidents) y (percentage of all fatal accidents) 60 50 50 10 10 10 15 20 25 30 35 40 5 10 15 20 25 30 35 40 50 GO TO 80 40 50 O xtape in years)) x tage (in years)) x tage (in years)) xtage (in years)) (b) Verify the given sums Ex, Ly, Ex", Ly', Exy, and the value of the sample correlation coefficient /. (Round your value for r to four decimal places.) Ex - 372 Ey - 112 EX- 8224 2 - 24814 Exy - 3120 - 0.9637 (c) Find x, and y. Then find the equation of the least-squares line y - a + by. (Round your answer to four decimal places.) x - 62 0800 V- 18 6067 - -26.6819 + 0.72147. [0.42/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.018.5. Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that It is possible to use the cricket as a ther or at Harvard. In the following data, x is a random variable representing chirps per s variable representing temperature ("F). X 20.4 94.7 15.0 17.2 16.0 69.4 83.3 79.6 6 80.6 LA USE SALT Complete parts (a) through (e), given Ex - 249.2, zy - 1203.4, Ex - 4185, By2 - 97,241.82, Exy - 20,138.19, and r = 0.8231. (a) Draw a scatter diagram displaying the data. 95 19 85 y (temperature (In degrees Fahrenheit (temperature (in degrees Fahrenheit y (temperature (In degrees Fahrenheit) y (temperature (In degrees Fahrenheit) 80 15 15 15 17 18 19 20 75 80 85 90 95 75 80 15 16 17 18 19 x (chirps per second) O * (chirps per second) x (chirps per second) * (chirps per second) b) Verify the given sums Ex, Ly, Ex-, Lyd, Exy, and the w Er. (Round your value for r to four decimal places.) Ex - 249.2 Ey - 1203.4 Ex - 20138.19 JX 22- 4185 x Exy - 97241.82 7x r - 0.8231 (c) Find x, and y. Then find the equation of the least-squares line $ - a + by. (Round your answer to four decimal places.) - 26 3836 + 2.2410 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y (temperature (in degrees Fahrenheit) y (temperature (in degrees Fahrenheit y (temperature (in degrees Fahrenheit y (temperature (In degrees Fahrenheit) 2 LL 15 16 17 18 19 70 75 80 90 95 80 15 16 19 20 x (chirps per second) x(chirps per second) (chirps per second) x (chirps per second) (e) Find the value of the coefficient of determination . What percentage of the variation in y can be explained by the come spanding variation in x and the least-squares line? What percent ge is unexplained? (Round your ans "wers for the percentages to two decimal place.) explained unexplained (f) What is the predicted temperature when x - 16.2 chirps per second? (Round your answer to two decimal places.)10. [0.78/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.021.5. (a) Suppose you are given the following (x, y) data pairs. X 1 3 4 2 1 8 LA USE SALT Find the least-squares equation for these data (rounded to four digits after the decimal). = -0.7143 + 1.8420 (b) Now suppose you are given these (x, y) data pairs. X 2 1 8 1 3 4 Find the least-squares equation for these data (rounded to four digits after the decimal). = 1.6860 + 0.2674 (c) In the data for parts (@) and (b), did we simply exchange the x and y values of each data pair? 0 Yes O No (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). X= -0.4348 1 X + -0.8086 X y11. [0.13/1 Points] DETAILS PREVIOUS ANSWERS BBUNDERSTAT12 9.2.025.S. Let x = boiler steam pressure in 100 lb/ in and let y = critical sheer strength of boiler plate steel joints in tons/ in . We have the following data for a series of factory boilers. 3.4 8 10 4.2 6.3 10.9 13.3 LO USE SALT (a) Make the logarithmic transformations x' = log (x) and y' = log (v). Then make a scatter plot of the (x, y') values. Does a linear equation seem to be a good fit to this plot? The transformed data does not fit a straight line well. The data seem to explode as x increases. The transformed data fit a straight line well. The transformed data does not fit a straight line well. The data seem to explode as x decreases. O The transformed data does not fit a straight line well. The data seem to have a parabolic shape (b) Use the (x, y') data points and a calculator with regression keys to find the least-squares equation y' = a + by'. What is the correlation coefficient? (Use 4 decimal places.) y'= -0.451 1 x + 1.600 1 x x (c) Use the results of part (b) to find estimates for a and @ in the power law y = ox". Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 4 decimal places.) B=