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Question 2 (q. 2.7, Page 78) - Theory You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N = 52 observations. (a) The estimated error variance ??² = 2.00. What is the sum of the squared least squares residuals? (b) The estimated variance of b? is 0.25, what is the standard error of b?? What is the value of ?(x? ? x?)²? (c) Suppose the dependent variable y? is the state's mean income (in thousands of dollars) of males who are 18 years of age or older and x? the percentage of males 18 years or older who are high school graduates. Interpret the slope estimate b?? = 0.10. (d) Suppose x? = 50.00 and y? = 10.00, what is the estimate of the intercept parameter? (e) Given the results in (b) and (d), what is ?x?²? (f) For the state of Arkansas the value of y? = 12 and the value of x? = 60. Compute the least squares residual for Arkansas. (Hint: Use the information in parts (c) and (d)). Solution (a) (b) (c) (d) (e) (f)

          Question 2 (q. 2.7, Page 78) - Theory

You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N = 52 observations.

(a) The estimated error variance ??² = 2.00. What is the sum of the squared least squares residuals?

(b) The estimated variance of b? is 0.25, what is the standard error of b?? What is the value of ?(x? ? x?)²?

(c) Suppose the dependent variable y? is the state's mean income (in thousands of dollars) of males who are 18 years of age or older and x? the percentage of males 18 years or older who are high school graduates. Interpret the slope estimate b?? = 0.10.

(d) Suppose x? = 50.00 and y? = 10.00, what is the estimate of the intercept parameter?

(e) Given the results in (b) and (d), what is ?x?²?

(f) For the state of Arkansas the value of y? = 12 and the value of x? = 60. Compute the least squares residual for Arkansas. (Hint: Use the information in parts (c) and (d)).

Solution
(a)
(b)
(c)
(d)
(e)
(f)

Question 2 (q. 2.7, Page 78) - Theory

You have the results of a simple linear regression based on state-level data and the District of Columbia, a total of N = 52 observations.

(a) The estimated error variance ??² = 2.00. What is the sum of the squared least squares residuals?

(b) The estimated variance of b? is 0.25, what is the standard error of b?? What is the value of ?(x? ? x?)²?

(c) Suppose the dependent variable y? is the state's mean income (in thousands of dollars) of males who are 18 years of age or older and x? the percentage of males 18 years or older who are high school graduates. Interpret the slope estimate b?? = 0.10.

(d) Suppose x? = 50.00 and y? = 10.00, what is the estimate of the intercept parameter?

(e) Given the results in (b) and (d), what is ?x?²?

(f) For the state of Arkansas the value of y? = 12 and the value of x? = 60. Compute the least squares residual for Arkansas. (Hint: Use the information in parts (c) and (d)).

Solution
(a)
(b)
(c)
(d)
(e)
(f)

Added by Thomas F.

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