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 (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. х 6. |y 48 43 33 26 Complete parts (a) through (e), given Ex = 14, Ey = 150, Ex2 = 66, Ey2 = 5918, Exy = 455, and r= -0.992. (a) Draw a scatter diagram displaying the data. 55 Graph Layers Cleat All • Point 1 50 • Point 2 45 Fill • Point 3 40 • Point 4 35 No Solution 30 25 20 O Help WebAssign. Graphing Tool O Submission Data (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 three decimal places.) Ex = 14 Ey = 150 Ex = 66 Ey2 = 5918 Σγ2 Exy = 455 r= -0.992 (c) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) X= 3.5 y = 37.5 ý = 34 X* + -0.992 (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y 55 55 50 50 45 45 40 40 35 35 30 30 25 25 20 х 20 2 4 8 4 55 55 50 50 45 45 40 40 35 35 30 30 25 25 20 х 8. 20 4 6. 6. (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) 2 - -0.9 x explained unexplained (f) If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)

A researcher want to know if there is a relationship between sleep and anxiety.  The researcher randomly selected n = 5 participants and asked each to rate their sleep quality and anxiety level on a scale of 1 to 5.  The data are below: Sleep X  Anxiety Y 2 2 3 3 2 2 4 2 5 2 Calculate the Sum of Squares for X (SSX)

The height (sidewalk to roof) of notable tall buildings in America is compared to the number of stories of the building (beginning at street level). Stories (x) Height (y) 56 1050 29 428 26 362 40 529 60 790 22 401 38 380 110 1454 100 1127 46 700 Calculate the least squares line. Put the equation in the form of: ý = a + bx. (Round your answers to three decimal places.) 86.7405 12.195

A motorist found that the efficiency of her engine could be increased by adding lubricating oil to fuel. She experimented with different amounts of lubricating oil and the data are Amount of lubricating oil (ml) Efficiency (%) 0 25 50 75 100 | 60 70 75 81 84 (a) Obtain the least squares fit of a straight line to the amount of lubricating oil. (b) Test whether or not the slope B, = 0. Take a = 0.05 as your level of significance. (c) Construct a 90% confidence interval on the mean response at xo = 10 ml.