Can you please explain the answer ?
These are all the given information.
Here the response variable y is dependent on the input variable x which is a matrix of n by p order and each element of x is of dimension p. The matrix aT contains a0,a1,.......ap.
a0 is the y intercept and ap is the slope coefficient for each independent variable. And the term is the error term. So from the given equation we get the regression for each response variable as
Yi = a0 +a1x1+....... +apxp. +
Linear regression can only be used when one has two continuous variables—an independent variable and a dependent variable. The independent variable is the parameter that is used to calculate the dependent variable or outcome. A multiple regression model extends to several explanatory variables.
Can you please explain the answer ? These are all the given information. 1 Problem 1...
please help to solve that question very appreciate if you can help me to solve all the part as my due date coming soon but got stuck in this question. Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables...
Do I get the right answers? If not, can someone please explain? (a) 2 points possible (graded, results hidden) Consider a Gaussian linear model Y = aX + e in a Bayesian view. Consider the prior (a) = 1 for all a eR. Determine whether each of the following statements is true or false. (a) is a uniform prior. O True C False n(a) is a Jeffreys prior when we consider the likelihood L (Y = y|A = a, X...
please help me to solve part b and c . and please dont copy my answer in part a and then post it as an answer. thanks Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed...
The random vector Y = (Y1, ..., Yn)T is such that Y = Xβ + ε, where X is an n × p full-rank matrix of known constants, β is a p-length vector of unknown parameters, and ε is an n-length vector of random variables. A multiple linear regression model is fitted to the data. (a) Write down the multiple linear regression model assumptions in matrix format. (b) Derive the least squares estimator β^ of β. (c) Using the data:...
3. Consider the multiple linear regression model iid where Xi, . . . ,Xp-1 ,i are observed covariate values for observation i, and Ei ~N(0,ơ2) (a) What is the interpretation of B1 in this model? (b) Write the matrix form of the model. Label the response vector, design matrix, coefficient vector, and error vector, and specify the dimensions and elements for each. (c) Write the likelihood, log-likelihood, and in matrix form. aB (d) Solve : 0 for β, the MLE...
in a Bayesian view. Consider the prior π(a)-1 for all a e R Consider a Gaussian linear model Y = aX+ E Determine whether each of the following statements is true or false. π(a) a uniform prior. (1) (a) True (b) False L(Y=y14=a,X=x) (2) π(a) is a jeffreys prior when we consider the likelihood (where we assume xis known) (a) True (b)False Y-XB+ σε where ε E R" is a random vector with Consider a linear regression model E[ε1-0, E[eErJ-1....
please help me to solve that question Consider two separate linear regression models and For concreteness, assume that the vector yi contains observations on the wealth ofn randomly selected individuals in Australia and y2 contains observations on the wealth of n randomly selected individuals in New Zealand. The matrix Xi contains n observations on ki explanatory variables which are believed to affect individual wealth in Australia, and he matrix X2 contains n observations on k2 explanatory variables which are believed...
3. In the multiple regression model shown in the previous question, which one of the following statements is incorrect: (b) The sum of squared residuals is the square of the length of the vector ü (c) The residual vector is orthogonal to each of the columns of X (d) The square of the length of y is equal to the square of the length of y plus the square of the length of û by the Pythagoras theorem In all...
Linear algebra problem: Please show all steps and explain, ensuring the given answer is correct. Question 7: Write the system of linear equations in the form Ai , where A is a matrix of the coefficients of the left-hand side of the system, v is the vector of the unknowns, and b is the vector of the constants of the right-hand side of the system
6. This problem considers the simple linear regression model, that is, a model with a single covariate r that has a linear relationship with a response y. This simple linear regression model is y = Bo + Bix +, where Bo and Bi are unknown constants, and a random error has normal distribution with mean 0 and unknown variance o' The covariate a is often controlled by data analyst and measured with negligible error, while y is a random variable....