Consider the multiple regression model with three independent variables, under the classical linearmodel assumptions MLR.1 through MLR.6:y = Bo + Bixi + Bzx2 + Bztz + u.You would like to test the null hypothesis H,: B1 – 3B2 = 1.(i) Let Bj and B denote the OLS estimators of ß1 and B,. Find Var(ß – 3B,) in terms of the vari-ances of Bj and Bz and the covariance between them. What is the standard error of Bi – 3B?|(ii) Write the t statistic for testing Họ: B1 – 3B2 = 1.|(iii) Define 0, = Bi – 3B2 and ô, = B1 – 3B. Write a regression equation involving Bo. 01. B2-and Bz that allows you to directly obtain ô, and its standard error.

Given: Consider the multiple linear regression models with three independent variables as given…

Answered: Consider the multiple regression model…

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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Consider the regression equation with quantitative predictor variable x1 and indicator variables x2 and x3, corresponding to one qualitative predictor variable. Interpret the hypothesis H0: β2 = 0 in terms of the regression lines associated with the three possible values of the qualitative predictor variable.
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
After studying the milk yields of a randomly selected sample of 900 cows, researchers felt that the presence of white spots (WS,) on a cow's body led to a different level of milk production (MP). The researchers estimate the OLS regression: Question He MP = 5.36 +0.12×WS;, (2.23) (0.08) where WS, is a binary variable of the form: 1, if the cow has white spots WS, = { 0, if the i" cow doesn't have white spots The 95% confidence interval for the coefficient B, is ( ). (Round your answers to four decimal places.) Based on this interval, we will Vthe hypothesis B, = 0 at the 5% significance level. Which of the following statements describes the way in which the coefficient of the indicator variable could be interpreted in this case? A. The coefficient is the rate of change in the milk production due to a unit change in the number of cows with white spots. B. The coefficient of the indicator variable is the slope of the regression equation. C. The coefficient is the difference between the…
assume the final regression equation from the stepwise regression analysis of the dependent variable cost (C) and the 10 potential independent variables is as follows: C = -5000 + 75 D + 0.4 S - 130 PT + 100 NE Given that the final model is valid, interpret the coefficient of NE: On average, a plant constructed in northeast region of USA costs _____ than a plant constructed in other regions, while keeping other variables constant A) 100 dollars more B) 100 millions of dollars more C) 100 millions of dollars less D) 100 dollars less
An economist estimates the following regression model:y = β0 + β1x1 + β2x2 + εThe estimates of the parameters b1 and b2 are not very large compared with their respective standard errors. But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent variables.Having obtained these results, the economist strongly suspects the presence of multicollinearity. Since his chief interest is in the influence of X1 on the dependent variable, he decides that he will avoid the problem of multicollinearity by regressing Y on X1 alone.Comment on this strategy.
3
y 6. For this problem, use a linear regression model. 1 2 12 a) Use the correlation formula to the right to calculate the correlation R - 1 Sx Sy 11 п-1 n 8 14 SSR = 1 SST SSE 11 17 Coefficient of Deternination → R2 SST 14 16 b) Find R^2 using SSR/SST SST = v- 7)² Sum of Squares Total → 17 20 19 24 Sum of Squares Regression → SSR = 20 22 SSE = >v-y)? Sum of Squares Error → 25 27 c) Find the slope using the formula to the right -- Σ-3-) Slope a= d) Verify your answers to parts a,b,c using another method of your choice intercept b= y-ax where overbar denotes average e). Find the residual for x = 14 f) Use your regression equation to find the probable x-value for y = 83, you may round your answer to 2 decimal places. %3D
Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?b) Suppose x2 increased by 2 units. What would be the expected change in x1?c) Suppose x2 decreased by 4 units. What would be the expected change in x1?
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