A certain experiment produces the data (0,10), (1,12), (2,15). Describe the model that produces a least-squares fit of these points by a function of the form y-Acosx+Bsinx
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- Find the equation y = Bo + B,x of the least-squares line that best fits the given data points. %3D (-1,0), (0,2), (1,4), (2,7) The line is y =D+ Ox. (Type integers or decimals.)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.A certain experiment produces the data (1,7 2), (2,5.2), and (3, - 0.5). Describe the model that produces a least-squares fit of these points by a function of the form y A cos x B sin x The model is y = XB + e, where y = %3D V and e = eE, (Type an exact answer.)
- Consider the data points (2,7) and (3,4). (a) Find the straight line that provides the best least-squares fit to these data. (b) Use the slope and point-slope form to find the equation of the straight line passing through the two points. (c) Explain why it could have been predicted that the straight line in (b) would be the same as the straight line (a)A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. The following scatterplot shows the height, in centimeters (cm), and the foot length, in cm, for each high school senior from the sample. The least-squares regression line is shown. The computer output from the least-squares regression analysis is also shown. Term Coef(SE) CoefT-ValueP-Value Constant 105.086.0017.510.000 Foot length 2.5990.23810.920.000 S=5.90181R–sq=65.42% (a) Calculate and interpret the residual for the high school senior with a foot length of 20cm and a height of 160cm. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete image Question 2 (b) The standard deviation of the residuals is s=5.9. Interpret the value in context. BoldItalicUnderlineSuperscriptSubscriptUndoRedoΩBullet listNumbered listImage (12 image limit) Edit imageView imageDelete…In a study, nine tires of a particular brand were driven on a track under identical conditions. Each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. Tread depth is measured in "mils." Here, 1 mil is 0.001 inch. The equation of the least-squares regression line is: y-hat 360.64 - 11.39x Also, r = 0.9762. For every 1,000 miles driven, the decrease in tread depth (in mils) can be estimated as: 246.74 mils. 11.39 mils. 275.6 mils. O 360.64 mils.
- Consider the set of points (0,9),(1,5),(6,3) and (9,2). In this set of points, the age of a dolphin is the first part of each ordered pair and the second part is the number of tricks that the dolphin learned in a month. So, the 6 year-old dolphin learned 3 tricks in the month. Write the least squares regression line for this data. Use the line to estimate how many tricks a 4 year-old dolphin could learn. Then find r and r2. Explain what r2 means.Find the least squares regression line for the points {(-2, –5), (2, –1), (3, 2), (4, 7)}.estion 7 of 15 Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (°F), as the explanatory variable and the number of ice bags sold on as the response variable. The least squares regression (LSR) line for the data is y = -114.05 +2.17x. On one of the observed days, the temperature was 82 °F and 66 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, ŷ, when the temperature is 82 °F. Enter your answer as a whole number, rounding if necessary. ice bags Using the predicted value you just found, compute the residual at this temperature. residual = ice bags DOLL