In a regression based on 30 annual observations, U.S. farm income was related to four in-dependent variables-grain exports, federal government subsidies, population, and a dummyvariable for bad weather years. The model was fitted by least squares, resulting in a Durbin-Watson statistic of 1.29. The regression of e on ŷ yielded a coefficient of determination of0.043.(a) Test for heteroscedasticity.(b) Test for autocorrelated errors.

Given that: Number of observations, n = 30 Durbin Watson statistic, d = 1.29 Coefficient of…

Answered: In a regression based on 30 annual…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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In a regression based on 30 annual observations, U.S. farm income was related to four independent variables—grain exports, federal government subsidies, population, and a dummy variable for bad weather years. The model was fitted by least squares, resulting in a Durbin-Watson statistic of 1.29. The regression of e2i on ŷi yielded a coefficient of determination of 0.043.a. Test for heteroscedasticity.b. Test for autocorrelated errors.
Are the following statements true or false? Explain your answer.a. “An ordinary least squares regression of Y onto X will not be internallyvalid if Y is correlated with the error term.”b. “If the error term exhibits heteroskedasticity, then the estimates of Xwill always be biased.”
In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?
The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.
1) Indicate whether the following statements are true or false. Explain why and show your work.a) In a simple regression Yi = B1 + B2 Xi + ui where var(ui) = o^2.X^2, weighting the model by X would solve the problem of non-common (heteroskedastic) variance of the error term.
An econometrician suspects that the residuals of her model might be autocorrelated. Explain the steps involved in testing this theory using the Durbin–Watson (DW) test
An article included a summary of findings regarding the use of SAT I scores, SAT II scores, and high school grade point average (GPA) to predict first-year college GPA. The article states that "among these, SAT II scores are the best predictor, explaining 17 percent of the variance in first-year college grades. GPA was second at 15.2 percent, and SAT I was last at 13.1 percent." If the data from this study were used to fit a least squares line with y = first-year college GPA and x = high school GPA, what would the value of r2 have been? R2 ____________________%
Given the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?
The least-squares regression line relating two statistical variables is given as = 24 + 5x. Compute the residual if the actual (observed) value for y is 38 when x is 2. 4 38 2
Years of Work Experience and number of Job Offers of 10 job-seekers were as follows: Work Exp. 4 2 5 3 7 12 2 5 4 9 No. of Offers 7 1 8 4 13 19 3 11 9 15 a. Fit the regression equation of No. of Job Offers on Years of Work Experience. b. What will be the predicted number of offers for an applicant with 6 years of experience? c. Verify the relationship between the number of job offers and years of work experience using at least two relevant methods
Suppose the simple linear regression model, Yi = β0 + β1 xi + Ei, is used to explain the relationship between x and y. A random sample of n = 12 values for the explanatory variable (x) was selected and the corresponding values of the response variable (y) were observed. A summary of the statistics is presented in the photo attached. Let b1 denote the least squares estimator of the slope coefficient, β1. What is the value of b1?
A researcher notes that, in a certain region, a disproportionate number of software millionaires were born around the year 1955. Is this a coincidence, or does birth year matter when gauging whether a software founder will besuccessful? The researcher investigated this question by analyzing the data shown in the accompanying table. Complete parts a through c below. a. Find the coefficient of determination for the simple linear regression model relating number (y) of software millionaire birthdays in a decade to total number (x) of births in the region. Interpret the result. The coefficient of determination is 1.___? (Round to three decimal places as needed.) This value indicates that 2.____ of the sample variation in the number of software millionaire birthdays is explained by the linear relationship with the total number of births in the region. (Round to one decimal place as needed.) b. Find the coefficient of determination for the simple linear regression model…

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