wn and yields Y^ = 5.4 + 3.2X, R2 =0.26, SER=6.2 (3.1) (1.5)
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5. Suppose that (Yi,Xi) satisfies the least squares assumptions in Key Concept 4.3. A random sample of size n = 250 is drawn and yields
Y^ = 5.4 + 3.2X, R2 =0.26, SER=6.2
(3.1) (1.5)
(a)Test H0:β1 =0 vs. H1:β1 ̸=0 at the 5% level.
(b) Construct a 95% confidence interval for β1.
(c) Suppose you learned that Yi and Xi were independent. Would you be surprised? Explain.
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- When a least squares line is fit to the 11 observations in the service time data, we obtain SSE= 210.8204. Calculate s? and s. (Round s2 to 4 decimal places. Round s to 5 decimal places.) s^2 This is a numeric cell, so please enter numbers only.Given n pairs of observations on explained variable Y and explanatory variable X , econometrician chooses sample regression function (SRF) in such a way that the sum of the residuals Σe = Σ (yi – ŷ) is small as possible (a) Explain the problem of adopting criterion of minimizing Σe b) The problem of minimizing sum of the residuals can be avoided by adopting the least squares criterion. Explain the importance of adopting this method.Please answer as many as your allowed too. Thank you :) A regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x).The results of the regression were: ˆyy^=a+bxa=-1.68b=0.168 (a) Write the equation of the Least Squares Regression line of the formˆyy^= + x(b) Which is a possible value for the correlation coefficient, rr? -1.417 1.417 0.702 -0.702 (c) If a country increases its life expectancy, the happiness index will increase decrease (d) If the life expectancy is increased by 0.5 years in a certain country, how much will the happiness index change? Round to two decimal places.(e) Use the regression line to predict the happiness index of a country with a life expectancy of 69 years. Round to two decimal places.
- A recent random sample of 7 college graduates who found a job reported their GPA and entry-level salary (nearest thousand dollars). GPA 2.9 3.81 3.2 2.42 3.94 2.05 2.25 Salary 48 53 50 37 65 32 37 Find the least squares line if we consider GPA as the explanatory variable and salary as the response variable. (Round to 2 decimal places.)ˆyy^ = For a unit increase in GPA, how much more in Salary is predicted? (Round your answer to 2 decimal places.)What percentage of the variation in Salary (yy) can be explained by GPA (xx) and the least squares line? (Round to the nearest percent.)%A researcher collected data on the cholesterol level, CC, and the age, AA, of 24 people selected at random. Using the data, the researcher calculated the least-squares regression line to be Cˆ=182+2.2AC^=182+2.2A and the standard error of the slope to be 0.38. If the conditions for inference are met, which of the following is closest to the value of the test statistic to test the hypotheses H0:β=0H0:β=0 versus Ha:β≠0Ha:β≠0 ?Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s^2is known.Find the maximum likelihood estimator of b from first principles.Find the Score function, the estimating equation and the information matrix using GLM
- Heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: Var(et)=σt^2=σ^2 xt. But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: (Picture 1) Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do a different correction to get rid of it. (a) what correction would you use…Define Efficiency of GLS (generalized least squares) estimator?As what we learned, heteroskedasticity arises because of non-constant variance of the error terms. We said proportional heteroskedasticity exists when the error variance takes the following structure: var(et)=σt^2=σ^2xt But as we know, that is only one of many forms of heteroskedasticity. To get rid of that specific form of heteroskedasticity using Generalized Least Squares, we employed a specific correction – we divided by the square root of our independent variable x. And the reason why that specific correction worked, and yielded a variance of our GLS estimates that was sigma-squared, was because of the following math: var(et*)=var(et/(square root of xt))=1/xt * var(et)= 1/xt σ^2 xt= σ^2 Where var(et)=σ^2 according to our LS assumptions. In other words, dividing everything by the square root of x made this correction work to give us sigma squared at the end of the expression. But if we have a different form of heteroskedasticity (i.e. a difference variance structure), we have to do…
- Is the number of games won by a major league baseball team in a season related to the team's batting average? Data from 14 teams were collected and the summary statistics yield: Ey = 1,134 x= 3.642, =93,110, = 948622, and Txy = 295.54 Find the least squares prediction equation for predicting the number of games won, y, using a straight-line relationship with the team's batting average, x.Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i + e_i where e_i are independent and identically distributed N(0, variance_e) randon variables i = 1,...,2.tion 19.16. Random samples of 200 bolts manufactured by machine A and 100 bolts manufactured by machine B showed 19 and 5 defctive bolts respectively. Is there a significant difference between the performance of the two machines?