Homework Answers
i
tried my best please appreciate..??Add Answer to:
2. Suppose we are given data on n observations (x,Y), i 1,... , n, and we...
2. Suppose we are given data on n observations (zi, y), î i, . . ....
2. Suppose we are given data on n observations (zi, y), î i, . . . , n, and we have a linear model, so that E (Y,) = Ao +Ari. Let A = SXY/Sxx and A,-F-Ax be the least-square estimates given in lecture. (a) Show that E(SXY)-ASxx and E(y)-Ao +AT. (b) Use (a) to show that E (A)-A and E(A)-A- In other words, these are unbiased estimators (c) The fitted values Yī = β0+812 i are used as estimates...
2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and...
2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and we have a linear model, so that E(X) = β0+Axi. Let ßi-SXY/SXX and β0 = Y-Ax be the least-square estimates given in lecture. (a) Show that E(5xx) = ẢSXX and E(T) = β0+A2. (b) Use (a) to show that E(A) = and E(%) = A- In other words, these are unbiased estimators (c) The fitted values Y BotBr, are used as estimates of E(Y),...
Suppose we are given data on n observations (zi, Y4), i-1, . . . , n,...
Suppose we are given data on n observations (zi, Y4), i-1, . . . , n, and we have a linear model so that E(X)-β0+B1zi. Let A-SXY/SXX and A-Y-Aī be the least-square estimates given in lecture. (a) Show that E(Sxy)-ASxx and E(Y)-A +AF (b) Use (a) to show that E(BB and E(B)In other words, these are unbiased estimators (c) The fitted values Yi-A+Azi are used as estimates of %), and the residuals e,-x-Y; are used as surrogates for the unobservable...
2 2. Suppose we are given data on n observations (i, Y),, and we have a...
2
2. Suppose we are given data on n observations (i, Y),, and we have a linear model, so that E(X)-A, + ßiri-Let呙-SXY /SXX and β') = F-β,2 be the least-square estimates given in lecture (a) Show that E(SXY)-ASXX and E (T)-A] + β,7. (b) Use (a) to show that E(角)-βι and E(A) = 3). In other words, these are unbiased estimators. (c) The fitted values Yt = Atari are used as estimates of E(A), and the residuals e.-Yi for...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distr...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
4. We have n statistical units. For unit i, we have (xi; yi), for i-1,2,... ,n. We used the least squares line to obtain the estimated regression line у = bo +biz. (a) Show that the centroid (x, y) i...
4. We have n statistical units. For unit i, we have (xi; yi), for i-1,2,... ,n. We used the least squares line to obtain the estimated regression line у = bo +biz. (a) Show that the centroid (x, y) is a point on the least squares line, where x = (1/n) and у = (1/n) Σ¡ı yi. (Hint: E ) i-1 valuate the line at x = x. (b) In the suggested exercises, we showed that e,-0 and e-0, where...
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...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi ~ Exp(0.05/Xi), and provide the scatterplot of Y against X set.seed(123) n <- 500 <-rnorm (n, x 3, 1) Y <- rexp(n, X) (b) Fit the model Yi-Ao + Ax, + ε¡ using the lm function in R and provide a plot of the best fit line on the scatterplot of Y vs X, and the residual...
2. Suppose we are given data on n observations (zi, y), î i, . . . , n, and we have a linear model, so that E (Y,) = Ao +Ari. Let A = SXY/Sxx and A,-F-Ax be the least-square estimates given in lecture. (a) Show that E(SXY)-ASxx and E(y)-Ao +AT. (b) Use (a) to show that E (A)-A and E(A)-A- In other words, these are unbiased estimators (c) The fitted values Yī = β0+812 i are used as estimates...
2. Suppose we are given data on n observations (zi,Y), i = 1, , n, and we have a linear model, so that E(X) = β0+Axi. Let ßi-SXY/SXX and β0 = Y-Ax be the least-square estimates given in lecture. (a) Show that E(5xx) = ẢSXX and E(T) = β0+A2. (b) Use (a) to show that E(A) = and E(%) = A- In other words, these are unbiased estimators (c) The fitted values Y BotBr, are used as estimates of E(Y),...
Suppose we are given data on n observations (zi, Y4), i-1, . . . , n, and we have a linear model so that E(X)-β0+B1zi. Let A-SXY/SXX and A-Y-Aī be the least-square estimates given in lecture. (a) Show that E(Sxy)-ASxx and E(Y)-A +AF (b) Use (a) to show that E(BB and E(B)In other words, these are unbiased estimators (c) The fitted values Yi-A+Azi are used as estimates of %), and the residuals e,-x-Y; are used as surrogates for the unobservable...
2
2. Suppose we are given data on n observations (i, Y),, and we have a linear model, so that E(X)-A, + ßiri-Let呙-SXY /SXX and β') = F-β,2 be the least-square estimates given in lecture (a) Show that E(SXY)-ASXX and E (T)-A] + β,7. (b) Use (a) to show that E(角)-βι and E(A) = 3). In other words, these are unbiased estimators. (c) The fitted values Yt = Atari are used as estimates of E(A), and the residuals e.-Yi for...
4. (24 marks) Suppose that the random variables Yi,..., Yn satisfy Y-B BX,+ Ei, 1-1, , n, where βο and βι are parameters, X1, ,X, are con- stants, and e1,... ,en are independent and identically distributed ran- dom variables with Ei ~ N (0,02), where σ2 is a third unknown pa- rameter. This is the familiar form for a simple linear regression model, where the parameters A, β, and σ2 explain the relationship between a dependent (or response) variable Y...
4. We have n statistical units. For unit i, we have (xi; yi), for i-1,2,... ,n. We used the least squares line to obtain the estimated regression line у = bo +biz. (a) Show that the centroid (x, y) is a point on the least squares line, where x = (1/n) and у = (1/n) Σ¡ı yi. (Hint: E ) i-1 valuate the line at x = x. (b) In the suggested exercises, we showed that e,-0 and e-0, where...
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...
5) Consider the simple linear regression model N(0, o2) i = 1,...,n Let g be the mean of the yi, and let â and ß be the MLES of a and B, respectively. Let yi = â-+ Bxi be the fitted values, and let e; = yi -yi be the residuals a) What is Cov(j, B) b) What is Cov(â, ß) c) Show that 1 ei = 0 d) Show that _1 x;e; = 0 e) Show that 1iei =...
2. Suppose Y ~ Exp(a), which has pdf f(y)-1 exp(-y/a). (a) Use the following R code to generate data from the model Yi ~ Exp(0.05/Xi), and provide the scatterplot of Y against X set.seed(123) n <- 500 <-rnorm (n, x 3, 1) Y <- rexp(n, X) (b) Fit the model Yi-Ao + Ax, + ε¡ using the lm function in R and provide a plot of the best fit line on the scatterplot of Y vs X, and the residual...
Most questions answered within 3 hours.
-
After watching the lectures I am still having a hard time
understanding these equations.
1. The...
asked 38 minutes ago -
Testing:
H0:μ=56.9
H1:μ<56.9
Your sample consists of 23 subjects, with a mean of 56.3 and
standard...
asked 41 minutes ago -
straight wire, labeled as Wire A, lies horizontally on a
tabletop and is oriented to run...
asked 42 minutes ago -
For a Chi-Squared Goodness of Fit Test about a uniform
distribution, complete the table.
Round to...
asked 1 hour ago -
Milk of magnesia is only slightly soluble in water. Kc for the
reaction Mg(OHs)(s)>Mg2+(a) + 2OH-1(aq)...
asked 1 hour ago -
Excel's HYPGEOM.DIST function can be used to compute _____.
a. both hypergeometric probabilities and cumulative
hypergeometric...
asked 1 hour ago -
The rocket used for the human lunar missions was the Saturn V
rocket. At liftoff the...
asked 1 hour ago -
1. The East Street Bagel Shop has a weekly demand for 3,500
bagels, which they make...
asked 1 hour ago -
paraphrasing each paragraph
“Where two or more persons knowingly act together unlawfully,
the act of each...
asked 1 hour ago -
The lateral line system in fish is contained which of the
following?
chemoreceptors
photoreceptors
mechanoreceptors
odor...
asked 1 hour ago -
Find the y-intercept of y =-5 x. The y-intercept of y equals
negative 5 x is______...
asked 1 hour ago -
Customers arrive randomly at a gas station at the average rate
of 30 per hour, while...
asked 1 hour ago