3.3 #7 In Problems, fit the data with the models given, using least squares. a. y = b + ax b. y = ax² X y 1 1 2 3 1 2 4 2 5 4
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Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares…
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Q: We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares…
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- We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Сoef SE Coef T P Constant 317.43 28.31 11.24 0.002 Elevation -31.272 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ý = a + bx. (a) Use the printout to write the least-squares equation. (b) For each 1000-foot increase in elevation, how many fewer frost-free days are…. Find the equation for the least-squares line for the following table: x 6 20 0 14 25 16 28 18 10 18 y 15 31 10 16 28 20 40 25 12 15 Also calculate the coe cient of determinationcan you answer parts d and e
- You may need to use the appropriate technology to answer this question. Suppose data on advertising expenditures and revenue (both in thousands of dollars) for a certain restaurant follow. Advertising Expenditures Revenue 19 2 33 4 43 39 10 53 14 53 20 54 (a) Let x equal advertising expenditures (in thousands of dollars) and y equal revenue (in thousands of dollars). Use the method of least squares to develop a stralght line approximation of the relationship between the two variables. (Round your numerical values to two decimal places.)What is the solutiionThe 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 R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. Weight |(pounds), x Miles per 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 27
- A statistician wishes to examine the relationship between average monthly rainfall (in mm), x, and number of road accidents, y, in a particular city. The following calculations have been done for you: Ex = 276, Ex2 = 6888, Ey = 193, Ey 3421, Exy 4842 and n 12. !3! The equation of the least squares regression line is given byI need help with c, d, and e, please.Hello there, can you help me solve the problem with two subparts (b and c) Problem: (the image is attached) Subparts: b. Find the least-squares curve of the form above to fit the data (4, 1.57), (6, 2.05), (8, 2.5), (10, 2.7), (12, 3.1), (14, 3.6), (16, 3.8), and (18, 4.35), where x and y represent sales and costs in thousands. Produce a graph that shows the data pts and the graph of the cubic approximation. y = __x + (__)x2 + (__)x3 c. (the image is attached)
- 5. Use least-squares regression to fit a straight line to data given in table. Show data and line in the same graph. Give equation of the fitted line. 0 3 9 15 17 5 6 9 11 12 X y 5 7 V(knots) 6 7 9 P (kW) 170 270 400 560 12 8 6. Fit a straight line, a parabola and a cubic equation to the speed power data of a ship. Compare your results. (use matlab, excel etc. to obtain graph and relation) 10 770 19 14 11 12 13 14 15 1030 1360 1800 2350 3100 7. Estimate the first derivative the function f(x) = e* cosx, at x=2.0 employing step sizes of h= 0.25. Use centered finite divided difference formulas with 2 and 4 point. Compare your results with true value. Estimate error, &t.Consider the following. x 1 2 3 4 y 4 6 9 13 (a) Find an equation of the least-squares line for the data. (Give each answer correct to 3 decimal places.)y = x +(b) Draw a scatter diagram for the data and graph the least-squares line.An article gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States. Find the equation of the least-squares line describing the relationship between y = medical cost and x = pollution. (Give the answer to two decimal places.) ŷ = Region North eBook Upper South Deep South West South Big Sky West Additional Materials Pollution Cost of Medical 30.0 922 31.8 898 32.1 975 26.8 979 30.4 959 40.0 906
