X1.424.229.167.929.59y4.1112.2828.6224.8229.82YiFind estimates for the linear model y; = Bo+Bixi+e; where €; ~ N(0,0²).That is find Bo, 61, 6. Also perform a test of the null hypothesis HoB₁ = 0 at level a = = 0.01.

The regression line is used to make predictions. It has two types of variables and two types of…

Answered: 1.42 4.11 4.22 12.28 9.16 28.62 7.92…

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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b) Suppose you are given the following information for an OLS regression: Σχι X; Y = 830102,T = 22,x=416.5, y = 86.65, x = 3919654, RSS = 130.6 i) Calculate the ordinary least square regression line. Calculate SE (a) and SE (B) Perform the hypothesis test such that Ho: a = -60 versus H₁: α = -60 Perform the hypothesis test such that Ho: P = 0.4 versus H₁: B = 0.4 In both cases use a significance of 5%. ii) iii) iv)
4. The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between students' academic performance api00 with variable enroll which is the number of students in the school. Call: Im (formula = api00 enroll, data = d) Residuals: мin 10 Median 30 Маx -285.50 -112.55 -6.70 95.06 389.15 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 744.25141 15.93308 46.711 < 2e-16 *** enroll -0.19987 0.02985 -6.695 7.34e-11 *** --- Signif. codes: O ' *** ' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 135 on 398 degrees of freedom Multiple R-squared: 0.1012, Adjusted R-squared: F-statistic: 44.83 on 1 and 398 DF, p-value: 7.339e-11 0.09898
Consider the paired data: I 1.42 y 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Eį Find estimates for the linear model y = Bo+812, +e, where ~ N(0,0²). That is find 3o. 31, à. Also perform a test of the null hypothesis Ho 3₁ = 0 at level a = 0.01.
22. In a regression model involving 45 observations, the following estimated regression equation was obtained . Y =29+18X 1 +43X 2 +87X 3 +15X 4 For this model SSR = 400 and SST = 1000 The MSR for the above model is A. 10 B. None C. 100 D. 150 E. 40
Consider the following population model for household consumption: cons = a + b1 * inc+ b2 * educ+ b3 * hhsize + u where cons is consumption, inc is income, educ is the education level of household head, hhsize is the size of a household. Suppose a researcher estimates the model and gets the predicted value, cons_hat, and then runs a regression of cons_hat on educ, inc, and hhsize. Which of the following choice is correct and please explain why. A) be certain that R^2 = 1 B) be certain that R^2 = 0 C) be certain that R^2 is less than 1 but greater than 0. D) not be certain
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6. Suppose we estimate a linear regression equation Y; = Bo + B1X; + u; by OLS. (a) Show thatE ûi 0, where the û;'s are the regression residuals. i3D1 (b) Suppose we regress X; on û; by OLS, including a constant term in the regression. Show that the estimated coefficient on û; is equal to zero. (c) Suppose we regress Y; on the predicted value Y; by OLS, including a constant term in the regression. Show that the estimated coefficient on Y; is equal to one. (Hint: the regression residual is defined by û; = Y; – Y; where the predicted value Y; = Bo + B,X;. Here, Bo and B1 are the OLS estimators.)

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1.42 4.11 4.22 12.28 9.16 28.62 7.92 24.82 9.59 29.82 Find estimates for the linear model yi N(0,0²). Bo+Bixi +Ei where ei ~ That is find Bo, B1, 6. Also perform a test of the null hypothesis Ho B₁ = 0 at level a = 0.01. 1