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Problem 5 a. Suppose that a time-series regression model, y~ x₁ + t, was fitted to 40 data points, and the Durbin-Watson statistic was found as 3.28. Are the error terms independent? Apply the Durbin- Watson test (state the hypothesis, critical values, conclusion, etc.) to test positive and/or negative correlation. b. A linear regression analysis for a transformed model was studied: y* =y¹/³. If a 95% prediction interval for y* is (2.0, 3.0), find the 95% prediction interval for y. c. True or False? The presence of unusual observations may affect the slope of the regression line as well as the significance of the independent variable. d. True or False? The presence of multicollinearity affects the sizes and the signs of coefficients, but does not affect the significance of the independent variables. e. True or False? Suppose you solved a first-order linear regression model: y~ x₁ + x2 + x3 + x4. If VIF values of those independent variables are 1.33, 18.22, 18.69, and 1.62, respectively, multicollinearity will be detected.

Problem 5 a. Suppose that a time-series regression model, y~ x₁ + t, was fitted to 40 data points, and the Durbin-Watson statistic was found as 3.28. Are the error terms independent? Apply the Durbin- Watson test (state the hypothesis, critical values, conclusion, etc.) to test positive and/or negative correlation. b. A linear regression analysis for a transformed model was studied: y* =y¹/³. If a 95% prediction interval for y* is (2.0, 3.0), find the 95% prediction interval for y. c. True or False? The presence of unusual observations may affect the slope of the regression line as well as the significance of the independent variable. d. True or False? The presence of multicollinearity affects the sizes and the signs of coefficients, but does not affect the significance of the independent variables. e. True or False? Suppose you solved a first-order linear regression model: y~ x₁ + x2 + x3 + x4. If VIF values of those independent variables are 1.33, 18.22, 18.69, and 1.62, respectively, multicollinearity will be detected.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 5EA
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Problem 5 a. Suppose that a time-series regression model, y~ x₁ + t, was fitted to 40 data points, and the Durbin-Watson statistic was found as 3.28. Are the error terms independent? Apply the Durbin- Watson test (state the hypothesis, critical values, conclusion, etc.) to test positive and/or negative correlation. b. A linear regression analysis for a transformed model was studied: y* =y¹/³. If a 95% prediction interval for y* is (2.0, 3.0), find the 95% prediction interval for y. c. True or False? The presence of unusual observations may affect the slope of the regression line as well as the significance of the independent variable. d. True or False? The presence of multicollinearity affects the sizes and the signs of coefficients, but does not affect the significance of the independent variables. e. True or False? Suppose you solved a first-order linear regression model: y~ x₁ + x2 + x3 + x4. If VIF values of those independent variables are 1.33, 18.22, 18.69, and 1.62, respectively, multicollinearity will be detected.
Transcribed Image Text:Problem 5 a. Suppose that a time-series regression model, y~ x₁ + t, was fitted to 40 data points, and the Durbin-Watson statistic was found as 3.28. Are the error terms independent? Apply the Durbin- Watson test (state the hypothesis, critical values, conclusion, etc.) to test positive and/or negative correlation. b. A linear regression analysis for a transformed model was studied: y* =y¹/³. If a 95% prediction interval for y* is (2.0, 3.0), find the 95% prediction interval for y. c. True or False? The presence of unusual observations may affect the slope of the regression line as well as the significance of the independent variable. d. True or False? The presence of multicollinearity affects the sizes and the signs of coefficients, but does not affect the significance of the independent variables. e. True or False? Suppose you solved a first-order linear regression model: y~ x₁ + x2 + x3 + x4. If VIF values of those independent variables are 1.33, 18.22, 18.69, and 1.62, respectively, multicollinearity will be detected.
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