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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We want to write the least-squares equation ý a+ bx, using the given printout. Predictor Coef SE Coef Constant 316.27 28.31 11.24 0.002 Elevation -32.660 3.511 -8.79 0.003 S 11.0603 R-iq 95.1N Recall that a is the intercept and b is the slope of the line. Since the elevation is the explanatory variable, x, the coefficient of the x-term is the slope of the line. From the printout, this corresponds to the table value in the "Elevation" row, and "Coef" column. Therefore, The intercept is given by the value of the constant term. There is no variable, but the Minitab printout classifies this value as a "coefficient." (Note: This may or may not coincide with your previous experience with the terms "constant" and "coefficient," but it is mathematically correct for reasons that we will not explore in this tutorial.) The value in the "Constant" row and "Coef" column is 316.27, Therefore, a Substitute these values into the least-square equation. 9 -a+ bx
You are given the following information about y and x. y Dependent Variable Independent Variable Oa. 1 Ob. 5 Oc. -1 Od. 6 5 4 X 3 2 1 1 2 3 4 5 The least squares estimate of b₁ (slope) equals
The equation of the least-squares regression line is ý = 68.5 + 11.4x, where ý is the number of students enrolled and x is number of years the school has been The number of students enrolled at a school varies from year to year. For the first eight years the school is open, the number of students enrolled is recorded in the table shown. open. Which shows the residual plot? Students 92 Year 2. 94 100 104 80 4 60 113 131 40 7. 8. 147 176 20 -20 0. 2. 4. 8. Number of Years 3. 56
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 P Constant 315.27 28.31 11.24 0.002 Elevation -31.812 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.8% 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 = + x (b) For each 1000-foot increase in elevation,…
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 P Constant 316.62 28.31 11.24 0.002 Elevation -30.516 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.2% The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Round your answer to four decimal places.) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares…
The following data are provided: 1 2 3 5 y 2.2 2.8 3.6 4.5 5.5 You want to use least-squares regression to fit this data with the following model, b y = 1+ ax +- Determine the coefficients a, & b. 4-
Exhibit 14-25 You are given the following information about x and y. Independent Variable Dependent Variable 0.321 -0.321 Refer to Exhibit 14-25. The least squares estimate of b₁ (slope) equals -5.78 3 7 1.56 3 6 7 8 6 7 3 8
Complete parts (a) through (h) for the data below. 30 40 50 60 70 y 90 87 82 74 Question Help v 62 (c) Graph the line found in part (b) on the scatter diagram. Choose the correct graph below. O A. OB. Ay 80- OC. Ay 80- OD. Av 20- 20 20 80 100 (d) By hand, determine the least-squares regression line. /Dound to throo donimal lncon an nondod Click to select your answer(s). M acer 9 esc # 2$ 6. 4 3 e W k h
Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent variable.) (-1, 2), (1, 1), (3,-2) y 2 w|N 3 - X X
explain into details. Thank you.
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 =

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You are given the following information about x and y. x Independent Variable y Dependent Variable 1 5 2 4 3 3 4 2 5 1 The least squares estimate of Bo( intercept) equals?