6. Consider the following univariate regression model without a constant, Y₁ = 3x X₂ +E;. If you estimatethis model with the OLS method,[a] the sample average of Y₁ (Y = ₁ Y₁/N) will always be equal to the sample average of the predictedvalues from the OLS estimator, Ý, where Y₁ = BOLS X X₁[b] the sample mean of the residuals will not always be equal to zero[c] the sample covariance of X and the residual will not always be equal to zero[d] the sample mean of the residuals will always be positive[e] none of the above

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Answered: 6. Consider the following univariate…

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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29)
25. In a partially destroyed record, for the estimation of the two Iines of regression from a bivariate data (X, Y), the following results were available: Coefficient of regression of Y on X =-1-6 Standard error of the estimate of Y on X 3 Coefficient of regression of X on Y =-04 Find: (1) Coefficient of correlation between X and Y. (iii) Standard error of the estimate of X on Y. (ii) Standard deviations oy and Oy
Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
Suppose that I want to estimate the effect of x₁ on y. Consider the univariate regression line: how to calculate a and b₁ using OLS? y = a + b₁x₁
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
Suppose that you perform a hypothesis test for the slope of the population regression line with the null hypothesis H0: β1 = 0 and the alternative hypothesis Ha: β1 ≠ 0. If you reject the null hypothesis, what can you say about the utility of the regression equation for making predictions?
5
4. In a statistical investigation the grade point average (y) and study hour (x) of a group of students are observed as follows: Study hour (x) Grade point (v) 12 17 16 14 11 13 15 3.0 3.2 3.5 4.0 3.8 2.7 3.4 i) Fit a line of y on x and test the significance of regression. ii) Estimate y if x = 17.
Consider a simple regression Y = B1 + B2 X + u. Suppose we found out that the variance of error term is changing with larger values of X (heteroscedasticity). Show how you overcome the problem of heteroscedasticity by using White’s heteroscedasticity consistent variances (only for variance of the slope estimate). Show and explain.
In this problem you will perform calculations by hand, do not use the R functions lm() or anova() to find the results. Suppose our sample data consists of the six (x,y) pairs {(2,5), (4,6), (5,5), (7,10), (8,9), (10,13)}. Find Determine the fitted regression equation for this data, and use it to predict y for x=2, 4, 5, 7, 8, and Find the error associated with each of these predictions. Find Use the results from part (a) and (c) to calculate the coefficient of determination. What percentage of the variation in y is explained by the regression?
Suppose we carry out a linear regression analysis with the following model: Y = Bo + B1X1 + .. + BrXr + € where k = 8. n = 195. We find SSReg = 231.4, and SSTotal = 972.5. Before collecting the data, we knew that we'd like to test the null hypothesis that Bi = B2 = 63 = 0. If we run a regression model leaving the predictors associated with these slopes out of the model, we find SSReg = 74.1 and SSTotal = 972.5. What is the value of the appropriate Fstatistic to test this null hypothesis (that these 3 slopes are 0)?
3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years). The data appears in the table below. year of bottling price a) draw the scatter diagram showing how wine price varies by vintage year b) use the most appropriate regression equation to determine the relationship between year of bottling (age) and price. c) what is the explanatory power (RSQ) of that equation d) determine the predicted price of a bottle of this wine for the 2017 vintage. 2009 36 2010 40 2011 51 2012 60 2013 68 2014 72 2015 70 2016 65 2018 51 2019 44 2020 39

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