7. The least square curve of the form y = ab* to the following data2348.315.433.1is(a) y = 3 ex ln2(c) y = 3 e2 lnxO aO bO cO dXy5 665.2 127.4(b) y = 3 (2)*(d) None of the above

Hint: Substitute the given values in the given options and identify the correct one.

Answered: 7. The least square curve of the form y…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 2. Show that, for a simple linear regression, R² = ry, where R² is the coefficient of determination and rxy is the sample correlation between Y and X. Hint: Σ" (Υ - Y)2 Σ1(Y₁-Y)²¹ SxY √SXXSYY' where Sxy = 1 (X; — X)(Y; — Y), Sxx = ₁1(X; - X)², Syy = ₁₁(Y₁ - Y)². R² = "XY =
The Answer is 3y = -x + 19
17. The equation of the regression line used in statistics is O A. x = a +by O B. y = bx +a %3D O C. y' = a + bx O D. x = ay +b
4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?
1) A historic data set on the relationship between car speed (X) and stopping distance (Y) is given in the R data cars. Use the R output given below to answer the following questions. Estimate Std. Error t value Pr(>|t|) (Intercept) -17.5791 6.7584 -2.601 0.0123 3.9324 0.4155 9.464 1.49e-12 Multiple R-squared: 0.6511 Analysis of Variance Table Df Sum Sq Mean Sq F value Pr (>F) 1 21186 1.490e-12 Residuals 48 11354 a) What is the sample size in this study? b) Give the estimate of the standard deviation of the intrinsic error. c) Give the values of the t-test statistics for testing Ho : Bo = 0 vs. Ha : Bo + 0 and H, : B1 = 0 vs. Ha : B1 # 0. What are the corresponding p-values? d) Fill in the missing entries in the ANOVA table. e) What proportion of the total variability of the stopping distance is explained by the regression model?
assessment.casa.uh.edu/Assessment/Root/Pages/TestTaker/Quiz.aspx?id=2F507231-0111-4CFC-8C26-F38ED05C3949 f) O None of the above Review Later Question 7 If the LSRL relating the independent variable x and the dependent variable y for a given problem is ŷ = 2x + 4, then an increase of 1 unit in x is associated with an increase of how many units in y? a) 06 b) 00 d) O1 e) 04 Review Late
3.1 Suppose X ~ N(18, 7). What value of x has a z-score of -2.16? Round to 2 decimal places..
The following Table summarizes the main estimation results for the below model: C- Bo + B,R + Balet E.where (C) denotes total household Consumption in SL, (R) is the national Incorme, and (1) denotes the Taxes collected from the private sector. The time span goes from 1974, 1st quarter, to 2010, 4th quarter and all the variables are expressed in million Rupees. Dependent variable C Constant R. Coefficient Sd. Eror t-statisties 128 40 3.2 0.90 0.48 0.67 6.0 32 0.15 0.15 R squared Residual Std. 1.35 Deviation Given the information in above table and the null that the Given the information in above table and the null that the Taxes collected from the private sector (B2) is not equal to zero, O a. There is not enough information to test this hypothesis. O b. The test statistic can be computed and the null is rejected in favor of the alternative hypothesis with a 5% significance. O . None cof the these O d. The test statistic can be computed and the null is not rejected in favor of the…
28 No Y Xi For the data in the table, YI = 83.8-5.2Xi; Whether the model has been estimated, answer the 1 54 5 2 47 8 following relevant questions accordingly: var (B2) =? 3 41 9. 4. 35 9. 28 11 6. 17 12 4,72 0,66 O 1,12 O 3,54 O 2,18 О
4.38
Suppose that n= 195 I.I.d. observations for (Y, X;) yleld the following regression results: v= 32.68 + 67.55Xx, SER= 18.63, R = 0.84 (15.7) (12.5) Another researcher is interested in the same regression, but he makes an error when he enters the data into the regression: He enters each observation twice, so he has 390 observations (with observation 1 entered twice, observation 2 entered twice, and so forth). Which of the following eatimated parameters change result? (Check all that apply) O A. The estimated intercept and slope. O B. The R of the regression. Yc. The standard error of the regrussion (SER). YD. The standard errors of the estimated coefficients. Using the 390 observations, what results will be produced by his regression program? Ý= 32.68 + 67.55X, SER =.R = 0.84 (Round your responses to two decimal places)
4.5. After fitting the regression model, y= Bo + Bix1 + Brx2+ B3x3+€ on 15 cases, it is found that the mean square error s? =3 and 0.5 0.3 0.2 0.6 0.3 6.0 0.5 0.4 (X'X)-' = 0.2 0.5 0.2 0.7 0.6 0.4 0.7 3.0 Find a. The estimate of V (ß1). b. The estimate of Cov(ß¡, ß3). c. The estimate of Corr(ß1, ß3). d. The estimate of V (ß¡ – B3).

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7. The least square curve of the form y = ab* to the following data is (a) y = 3 ex In2 (c) y = 3 e2 Inx O a O b O d X y 2 8.3 3 15.4 4 33.1 5 65.2 6 127.4 (b) y = 3 (2)* (d) None of the above