1. Derive the critical values of 3 and ₁ that minimize the residual sum of squares for the followingsample regression model Y₁ = Bo + B₁ Xi + êi2. Derive the critical values of do and ai that minimize the residual sum of squares for the followingsample regression model Y₁ = ao + ấ₁1 (Xi − X) + êi

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Answered: 1. Derive the critical values of 0 and…

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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A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2 for a sample of N=11N=11 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test statistics to assess the significance of the regression model and partial slopes. Use a significance level α=0.05α=0.05. X1X1 X2X2 YY 52.3 45.6 49.1 55.9 48.7 53.1 46.5 47.4 45.9 52 45.6 59.8 48.9 45.5 52.6 46.2 35.1 71.2 28.8 32.6 33.5 40.7 41 40.3 43.7 40 65.8 47 37.8 52.8 34.2 28 53.5 R2=R2= (Not the adjusted R2R2) FF test statistic = P-value for overall model = test statistic for b1b1 p-value for the two-tailed test = test statistic for b2b2 p-value for the two-tailed test = What is your conclusion for the overall regression model at the 0.05 alpha level (also called the omnibus test)? The overall regression model is statistically significant at α=0.05α=0.05. The overall…
Consider a simple linear regression model with predictor variable x and response variable y, where the regression line is represented by the equation y = β0 + β1x. If β0 = -5 and β1 = 3, what is the predicted value of y for a given x = 4?
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Which of the following is true of the least-squares regression line y = b1x + bo? Select all that apply. OA. The least-squares regression line always contains the point (x,y). B. The least-squares regression line always contains the point (0,0). O C. The predicted value of y, y, is an estimate of the mean value of the explanatory variable for that particular value of the response variable. O D. The least-squares regression line maximizes the sum of squared residuals. O E. The least-squares regression line minimizes the sum of squared residuals. O F. The sign of the linear correlation coefficient, r, and the sign of the slope of the least-squares regression line, b1, are the same. D G. The predicted value of y, y, is an estimate of the mean value of the response variable for that particular value of the explanatory variable. Click to select your answer(s) and then click Check Answer. Check Answer Clear All All parts showing acer esc $ 4
Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "Sample data." These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 14.87+0.88x. In the "Calculations" table are calculations involving the observed y-values, the mean y of these values, and the values y predicted from the regression equation. Sample data Calculations 160+ x y (x-1)² (-5)² (v-^^)² 150+ 107.2 110.7 396.0100 457.7032 2.2320 122.0 130.3 140- 0.0900 70.0569 65.1249 131.5 122.1 130- 72.2500 0.0001 72.0801 142.5 129.9 120. 0.4900 93.5089 107.5369 152.5 160.0 110- 864.3600 341.1409 119.4649 Send data to Excel LL 130 130 140 150 160 Column sum: 1333.2000 Column sum: 962.4100 Column sum: 366.4388 Figure 1 Answer the following. (a) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an…
Suppose that you have estimated coefficients for the regression model Y = B₁ + B₁X₁ + ß2X2 + ß3X3. Test the hypothesis that all three of the predictor variables are equal to 0, given the analysis of variance shown on the right. Use α = 0.05. Click here to view page 1 of a table of critical values of F. Click here to view page 2 of a table of critical values of F. Choose the correct null and alternartive hypotheses below. A. Ho: B₁ B₂ =B3 = 0 H₁: at least one ß; #0 C. Ho: B₁ B₂ = 3 = 0 H₁: B₁0, B₂0, B3 > 0 Find the critical value. The critical value is (Round to two decimal places as needed.) Source Regression Residual Error DF SS 3 9,654 23 2,400 B. Hō: at least one ß; ‡0 H₁: B₁ =B₂ =B3 = 0 D. H₁: B₁ = P₂ = ³3 = 0 H₁: B₁ B₂ B3 0 MS
4 Blank Filling Question. No work is required or graded. A simple linear regression analysis for n = 20 data points produced the following results: %D ŷ = 2.1 + 3.4x x = 2.5 y = 10.6 %D %D SS = 4.77 SSyy = 59.21 SSxy = 16.22 1. Find SSE, the sum of squares of residuals. SSE= SSyy %3D 2. Find s, the estimated standard error of the regression model. s2=SSE÷ and then taking square root will give s = 3. Find a 95% confidence interval for E(y) when x = 2.5. Xs.e.
A researcher wishes to investigate the association between two variables, denoted xi and yi. The following results have been obtained from the analysis of a sample of 30 observations: Sxi = 119.2, Syi = 129.2, Sxi yi = 480.9, xSi2 = 493.6 (xi −x)2 = 20.4, ei2 =444.2 Calculate the ordinary least squares (OLS) estimates of the coefficients of the linear regression, yi = β1 + β2xi +ui. What does your estimate of β2 in part (i) suggest about the association between xi and yi. Calculate the standard error of the regression, ˆ , and the standard error of the estimated slope coefficient, se(ˆ2) . Test the null hypothesis H0: 2=0 against the alternative hypothesis H1: 20, using a significance level of 0.05. On the basis of your hypothesis test in part (iv), is there any evidence of an association between xi and yi?
A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects. Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model. Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg= SSres= R2= F= P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…

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1. Derive the critical values of 0 and 3₁ that minimize the residual sum of squares for the following sample regression model Y₁ = 0 + ₁ Xi + ei