MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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. 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 determination
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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 Coef SE Coef T. Constant 317.97 28.31 11.24 0.002 Elevation -28.572 3.511 -8.79 0.003 S = 11.8603 R-Sq 94.2% %3D 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 ŷ = a + bx. (a) Use the printout to write the least-squares equation. %3D (b) For each 1000-foot increase in elevation, how many fewer frost-free days are…arrow_forwardComplete Table 3 and find the values of A and B for the straight line that provides the best least-squares fit to the data Table 3 y xy 1 2 3 7 4 9 5 12 Ex = Ey = Σxy Ex² =arrow_forwardWe 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 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 ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = 317.43 -31.272 (b) For each 1000-foot increase in elevation, how many fewer…arrow_forward
- Find the least squares approximating squares error for the points (1.1), (4.3). line and the least (2, 2), (3.2), andarrow_forwardTest the following data table to see whether the data are quadratic. x 0 4 16 32 44 y 4 12 16 12 20 Calculate the first-order and second-order differences.arrow_forwardThe 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) 59 1050 29 428 25 362 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: y = a + bx. (Round your answers to three decimal places.) ŷ = + Xarrow_forward
- NEED FULLY CORRECT HANDWRITTEN SOLUTION FOR THIS ASAP..... AND I'LL RATE POSITIVE FOR SURE.arrow_forwardA researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ý = 2-5z where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: O When amount of schooling increases by one year, the number of pregnancies tends to decrease by 5. O When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. ns O When amount of schooling increases by one year, the number of pregnancies tends to decrease by 2. re O When amount of schooling increases by one year, the number of pregnancies tends to increase by 2. urse Submit Question here to search 立arrow_forwardAn 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 906arrow_forward
- 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. 4 y 48 42 33 26 A USE SALT Complete parts (a) through (e), given Ex = 15, Ey = 149, Ex² = 77, Ey² = 5833, Exy = 489, and r= -0.9106. (a) Draw a scatter diagram displaying the data. 55 Graph Layers After you add an object to the graph you 50 can use Graph Layers to view and edit its properties. Fill 45 40 35 No Solution 30 25 20 O Help WebAssign. Graphing Tool ( b) Verify the given sums Σχ, Σγ, Σχ, Σy, Σχy, and the value of the sample correlation coefficient r. (Round your value forr to four decimal places.) Σχ Ey = Ex? = Ey? = Exy = r =arrow_forwardIt 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. x 1 2 5 6 y 48 41 33 26 Find the equation of the least-squares line = a + bx. (Round your answers to four decimal places.) = + xarrow_forward
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