7.If x1, X2 and x3three variates measured from theirarerespective means as origin and if e¡ is the expected value of x1 for givenvalues of x2 and x3 from the linear regression of x, on x2 and x3, prove thatcov (x1, e¡) = var (e¡) = var (x1) – var (x; - ei).||

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Answered: 7. If x1, x2 and x3 are three variates…

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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Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
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?
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
)A county real estate appraiser wants to develop a statistical model to predict the appraised value of 3) houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model: E(u) = Bo + Bix, where y = appraised value of the house (in thousands of dollars) and x = number of rooms. Using data collected for a sample of n = 73 houses in Fast Meadow, the following results were obtained: y = 73.80 + 19.72x What are the properties of the least squares line, y = 73.80 + 19.72x? A) Average error of prediction is 0, and SSE is minimum. B) It will always be a statistically useful predictor of y. C) It is normal, mean 0, constant variance, and independent. D) All 73 of the sample y-values fall on the line.
Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table. Length (mm) Weight (mg) Variable ?x ?y Insect 1 7 28 Insect 2 21 42 Insect 3 35 70 Derrick used the data to compute the least squares regression line. ?̂ =1.5?+15.167y^=1.5x+15.167 Calculate the residual value for each of Derrick's data points and the sum of the residual values. Report your answers precise to three decimal places. Residual 1: Residual 2: Residual 3: Sum of the residuals:
A statistics student is asked to estimate Y = Bo + B1X + E. She calculates the following values: Ex = 280, Σ(x₁ - x)² = 350, Σy, = 600, Σ(y, − y) = 1000 Σ(x,x)(y₁ - y) = -630, n = 20 Which of the following is the sample regression equation? OY--55.2-1.8X + e OY 55.2 +1.8X + e OY-55.2+1.8X + e OY 55.2 1.8X + e
We are researching the charity donation behaviour of Australians. We have the following model: (E1) Donate = β0 + β1Income +β2Avg_Gift + β3Edu + u Where: Donate is a dummy variable equal to 1 if the individual makes a donation in response to a social media campaign by our charity organisation, and 0 otherwise Income is the annual household income Avg_Gift is the average value of past donations made by the individual to our charity Educ is the individual's level of education (in years) Our data is a random sample of the population and we have 1,614 observations. You should assume E [u | Income, Avg_Gift, Educ] = 0. Using the information above, please answer the following 3 questions. [i] Referring to Model (E1) above, interpret the coefficient β1. [ii] You know that this model will suffer from heteroskedasticity. Why is this the case? Explain your reasoning. [iii] In your own words, what is heteroskedasticity?

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7. If x1, x2 and x3 are three variates measured from their respective means as origin and if e, is the expected value of x1 for given values of x2 and x3 from the linear regression of x, on x2 and x3, prove that cov (x1, e1) = var (ej) = var (x1) – var (x¡ - ei).