Example 17.8) Find the multiple linear regression of X, on X2 and X3 from the data relating to threevariables given below:X, :X2:X3:1038252916141239203116231023161311

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Answered: Example 17.8 Find the multiple linear…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
The following graphs show a least squares regression line plotted to different sets of data. Each of the linear models has a formula y = 0.500(x) + 3. For each model: • Describe how you would go about evaluating the appropriateness of the model, and the process you would go through to develop a valid predictive model. 14 14 14 12 12 12 10 10 10 8. 8. 6. 6. 4. 4 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20 2 4 6 8 10 12 14 16 18 20
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number of social science doctorates for each additional education doctorate. The slope tells us the increase in the number of social science doctorates for each additional education doctorate.…
Q.1 The Conference Board produces a Consumer Confidence Index (CCI) that reflects people’s feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers feel that consumer confidence is a function of median household income. Shown here are CCIs for 9 years and median household incomes for the same 9 years published by the U. S. Bureau of the Census. CCCI Income ($1000) a) Determine the equation of the regression line 8 37.415 used to predict the CCI from the median household 68.3 35.015 income 90.5 36.770 62.6 35.237…
7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannel
Consider the following data for a dependent variable y and two independent variables, x1 and x2. x1 x2 y 30 12 94 47 10 108 25 17 112 51 16 178 40 5 94 51 19 175 74 7 170 36 12 117 59 13 142 76 16 211 (a) Develop an estimated regression equation relating y to x1. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51. (Round your answer to one decimal place.) (b) Develop an estimated regression equation relating y to x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x2 = 19. (Round your answer to one decimal place.) (c) Develop an estimated regression equation relating y to x1 and x2. (Round your numerical values to one decimal place.) ŷ = Predict y if x1 = 51 and x2 = 19. (Round your answer to one decimal place.)
Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 4 12 14 20 23 30 40 47 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 46 38 46 53 75 82 99 104 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation isrunoff = -2.07 + 0.850 rainfall Predictor Coef Stdev t-ratio p Constant -2.067 2.412 -0.86 0.407 rainfall 0.85038 0.03708 22.93 0.000 s = 5.321 R-sq = 97.6% R-sq(adj) = 97.4% State the appropriate null and alternative hypotheses. H0: ?1 = 0 Ha: ?1 > 0 H0: ?1 = 0 Ha: ?1 ≠ 0 H0: ?1 = 0 Ha: ?1 < 0 H0: ?1 ≠ 0 Ha: ?1 = 0 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. (Use ? = 0.05.) Reject H0. There is a useful linear relationship…
Consider the following data on x = rainfall volume (m³) and y = runoff volume (m³) for a particular location. 7 12 14 17 23 30 40 49 55 67 72 83 96 112 127 4 10 13 15 15 25 27 46 38 46 53 70 82 99 103 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation is runoff = -2.00 + 0.841 rainfall Predictor Coef Stdev t-ratio Constant -2.000 2.194 -0.91 0.379 rainfall 0.84079 0.03369 24.96 0.000 s = 4.823 R-sg = 98.0% R-sq (adj) = 97.8% State the appropriate null and alternative hypotheses. O Ho: B1 = 0 H: B, 0 O Hoi Bq # 0 H: B1 = 0 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. (Use a = 0.05.) O Reject H.. There is a useful linear relationship between runoff and rainfall at the 0.05 level. O Reject H.. There is not a useful linear relationship…
(b.) Consider the fictitious set of data shown below, where the line through the data is the fitted simple linear regression line. Sketch a residual plot (It doesn't need to be perfect) on the right side of this graph. What type of transformation is needed to get a proper SLR model? Write the general form of this new SLR model. §
3. For the data provided in the given table Thermocouple 821 835 816 (x) 820 840 836 825 840 833 827 IR 818 834 824 821 845 830 819 843 832 835 measurement (y) a) Fit a simple linear regression model. b) Calculate the correlation coefficient.
Show that the following relationship on the simple linear regression class notebook is true: (Refer the image)
Suppose the analyst constructs the simple linear regression model In(y) = a + Bx+e. She estimates it to be In() = -1- 1.3x. What is the residual in Excel output for the pair of observations x= 1.5 and y = 27 O a. 6. O b. 1.98 O c. -2. O d. 403.43 e. 4.29

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Example 17.8 Find the multiple linear regression of X, on X2 and X3 from the data relating to three variables given below: X; : X2: X3 : 10 38 25 29 16 14 12 39 20 31 16 23 10 23 16 13 11