a) Create a scatter plot to verify that it is reasonable to assume that the regression of Y on x is linear. b) Fit a straight line using the method of least squares. c) Use the least squares method to estimate alpha

The table shows the number of goals allowed and the total points earned (2 polnts for a win, and 1 point for an overtme or shootout loss) by 14 lce hockey teams over the course of a season The equation of the regression line is (a) Find the coefficient of determination,, and interpret the result (b) Find the standard error of the estimate, and interpret the resut Goals Allowed, x Points, y -0.560x 218.067 Use he data to answer the folowing questions 217 213 221 229 260 262 277 205 216 20s 217 208 257 246 66 70 105 105 0 83 47106 103 97 9182 91 88 Inco (a) r-O (Round to three decimal places as noeded.)

Find the least squares regression line for the points: (0,0), (1,1), (2,5).

An article gave a scatter plot, along with the least squares line, of x = rainfall volume (m³) and y data on rainfall and runoff volume (n = runoff volume (m³) for a particular location. The simple linear regression model provides a very good fit to 15) given below. The equation of the least squares line is y = -2.364 + 0.84267x, ² 0.976, and s = 5.21. = x 5 12 14 17 23 30 40 47 55 67 72 81 96 112 127 y 3 9 12 14 14 24 27 45 38 46 52 71 81 100 101 (a) Use the fact that s = 1.43 when rainfall volume is 40 m³ to predict runoff in a way that conveys information about reliability and precision. (Calculate a 95% PI. Round your answers to two decimal places.) Ŷ 28.25 1x ) m³ Does the resulting interval suggest that precise information about the value of runoff for this future observation is available? Explain your reasoning. OYes, precise information is available because the resulting interval is very wide. 34.46 Yes, precise information is available because the resulting interval is very…

The table lists the average monthly cost to workers for family health insurance for various years. Year, x Average Monthly Cost to Workers for Family Health Insurance $298 a) Use a graphing calculator to fit a regression line to the data. b) Predict the average monthly cost to workers for family health insurance in 2020, and compare the value with $493.3, which is obtained using the points (1,340) and (4,386). c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely. 2009, 0 2010, 1 2011, 2 340 348 2012, 3 367 2013, 4 2014, 5 386 406 a) The linear equation of the regression line that best models the data is y =x+. (Round to the nearest hundredth as needed.) b) The average monthly cost to workers for family health insurance in 2020 is predicted to be $ (Round to the nearest cent as needed.) Compare the above obtained value with $493.3 This value is $ $493.3 c) The correlation coefficient is (Round to the nearest thousandth as…

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.

An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.