n regression, the two types of interval estimates concerning y are called
n regression, the two types of interval estimates concerning y are called
Homework Answers
In regression, the two types of interval estimates concerning y are called confidence interval and prediction interval.
A confidence interval is an interval that will contain a population parameter a specified proportion of the time.
In statistical inference, specifically predictive inference, a prediction interval is an estimate of an interval in which a future observation will fall, with a certain probability, given what has already been observed.
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n regression, the two types of interval estimates concerning y
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Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5<μ<13.1 with a...
Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5<μ<13.1 with a 95% level of confidence when σ is known. (i) Find the point estimates for the unknown population mean. (ii) Find the margin of error. (iii) Give the interpretation of the confidence interval. (iv) Name two ways of decreasing the width of the confidence interval. b) State the assumptions necessary for linear regression model Y=A+Bx+ε c) Let p^ be a sample proportion based on a...
Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5 < u...
Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5 < u < 13.1 with a 95% level of confidence when o is known. (1) Find the point estimates for the unknown population mean. (ii) Find the margin of error. (iii) Give the interpretation of the confidence interval. (iv) Name two ways of decreasing the width of the confidence interval. b) State the assumptions necessary for linear regression model Y = A + Bx + E...
answer this with concerning infrastructure projects cost estimates? (a). Screening estimates (order of magnitude es...
answer this with concerning infrastructure projects cost estimates?
(a). Screening estimates (order of magnitude estimates) are based on more detailed nformation when compared to preliminary estimates (conceptual estimates). Is this statement true or false? Explain your answer (b) List the various types of Design cost estimates of a construction project; put the list in an order of increasing accuracy with the first being the least accurate.
(a). Screening estimates (order of magnitude estimates) are based on more detailed nformation when...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector,...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector,...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
What are the two types of data used in regression analysis?
What are the two types of data used in regression analysis?
Correlation and Regression a) Determine the value of a (as a function of n and y),...
Correlation and Regression a) Determine the value of a (as a function of n and y), which minimizes S function given below. Prove your answer with all the details. s=30,-a)? b) Consider the following two models: Modell:Y, = B. +B,X, + u Model2:Y,= 2, + QX: +e; where Ñ =X; -X (i) Are the OLS estimators of constant terms for both models identical? Are their variances the same? Prove your answer. Are the OLS estimators of slope terms for both...
What is the intuition behind the answer? Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates...
What is the intuition behind the answer?
Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates of Bo and B1. If our regressions assumptions hold for the above specification. What is the relationship with the coefficients of the reverse regression x = ao + a1Yi + u;: (a) ao a CORRECT) - (b) @о — — Во = (с) dо — Во &1=-B1 (d) do — Во
Imagine that we run the regression y; =...
Interval estimates were produced for amount paid for travel by a state's Congressmen in the years...
Interval estimates were produced for amount paid for travel by a state's Congressmen in the years 2000 to 2005. Suppose the regression equation for the relationship between trip length x in days and amount paid y in dollars is ŷ = −669 + 1,178x. (a) Which interval should be narrower? The interval estimate of amount paid for an individual 5-day trip by a Congressman in the larger population. The interval estimate of mean amount for all 5-day trips taken by...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank k S11, E(c)-0 and E(es')-σ2Ω where Ω is a known non-singular matrix. The GiLS estimator of B is given by the formula Consider the following data 16 31 2 3 51 4 10 Assuming that Ay a) b) Calculate the GLS estimate of β in the model Y,Xß + ε Calculate the OLS estimate c) Compare it the two estimates and comment on efficiency.
Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5 < u < 13.1 with a 95% level of confidence when o is known. (1) Find the point estimates for the unknown population mean. (ii) Find the margin of error. (iii) Give the interpretation of the confidence interval. (iv) Name two ways of decreasing the width of the confidence interval. b) State the assumptions necessary for linear regression model Y = A + Bx + E...
answer this with concerning infrastructure projects cost estimates?
(a). Screening estimates (order of magnitude estimates) are based on more detailed nformation when compared to preliminary estimates (conceptual estimates). Is this statement true or false? Explain your answer (b) List the various types of Design cost estimates of a construction project; put the list in an order of increasing accuracy with the first being the least accurate.
(a). Screening estimates (order of magnitude estimates) are based on more detailed nformation when...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Considering multiple linear regression models, we compute the regression of Y, an n x 1 vector, on an n x (p+1) full rank matrix X. As usual, H = X(XT X)-1 XT is the hat matrix with elements hij at the ith row and jth column. The residual is e; = yi - Ýi. (a) (7 points) Let Y be an n x 1 vector with 1 as its first element and Os elsewhere. Show that the elements of the...
Correlation and Regression a) Determine the value of a (as a function of n and y), which minimizes S function given below. Prove your answer with all the details. s=30,-a)? b) Consider the following two models: Modell:Y, = B. +B,X, + u Model2:Y,= 2, + QX: +e; where Ñ =X; -X (i) Are the OLS estimators of constant terms for both models identical? Are their variances the same? Prove your answer. Are the OLS estimators of slope terms for both...
What is the intuition behind the answer?
Imagine that we run the regression y; = Bo+B1xe and recover the OLS estimates of Bo and B1. If our regressions assumptions hold for the above specification. What is the relationship with the coefficients of the reverse regression x = ao + a1Yi + u;: (a) ao a CORRECT) - (b) @о — — Во = (с) dо — Во &1=-B1 (d) do — Во
Imagine that we run the regression y; =...
2. In the regression model Y-Χβ+ E, Xis a fixed n x k matrix of rank k S11, E(c)-0 and E(es')-σ2Ω where Ω is a known non-singular matrix. The GiLS estimator of B is given by the formula Consider the following data 16 31 2 3 51 4 10 Assuming that Ay a) b) Calculate the GLS estimate of β in the model Y,Xß + ε Calculate the OLS estimate c) Compare it the two estimates and comment on efficiency.
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