Q. 21
The assumptions of the simple linear regression model include:
a. the errors are normally distributed
b. the error terms have a constant variance
c. the errors have a mean of zero
d. All of the above
e. a and c only
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Q. 21 The assumptions of the simple linear regression model include: a. the errors are normally...
Which of the following are assumptions for the linear regression model? CHECK THAT ALL MAY APPLY!!! Select one or more: a. Regression function (i.e., equation) is linear. b. Error terms are normally distributed. c. Error terms are independent. d. Error terms have constant variance. e. Regression model fits all observations (i.e., no outliers).
Q.8 In a regression model, the assumptions of the method of least squares include: [I] Relationship between x and y is linear [II] the values of X are fixed (non-random) [III] the error terms must be correlated with each other [IV] X is independent of Y [V] the error term is normal and is identically and independently distributed about the mean of zero [VI] the error term is normal but non random a. I, II, V b. II, III, VI...
What are the four primary assumptions of multiple linear regression (check all that apply)? Select one or more: a. Linear relationships between predictors and outcome b. Residuals are normally distributed with a mean of zero. c. There is constant variance of residuals d. The residuals are independent e. The predictors are normally distributed.
The model assumptions for multiple regression analysis are : 1. Normally distributed errors 2. Constant variance of the errors 3. Independent errors True False
(Do this problem without using R) Consider the simple linear regression model y =β0 + β1x + ε, where the errors are independent and normally distributed, with mean zero and constant variance σ2. Suppose we observe 4 observations x = (1, 1, −1, −1) and y = (5, 3, 4, 0). (a) Fit the simple linear regression model to this data and report the fitted regression line. (b) Carry out a test of hypotheses using α = 0.05 to determine...
7. In a simple regression model, suppose all of the assumptions of the classical linear regression morel apply, except that rather than assume E (ui | Xi) = 0, you assume that E (Ui / X;) = ali and E (xi) = 0 where a > 0 is a constant. (a) What is the conditional expectation of the OLS slope coefficient, i.e. E (B1 | 21, ..., XN)? (b) In this case, is ß1 an unbiased estimator of B1 or...
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....
2. Consider a simple linear regression model for a response variable Yi, a single predictor variable ri, i-1,... , n, and having Gaussian (i.e. normally distributed) errors Ý,-BzitEj, Ejį.i.d. N(0, σ2) This model is often called "regression through the origin" since E(Yi) 0 if xi 0 (a) Write down the likelihood function for the parameters β and σ2 (b) Find the MLEs for β and σ2, explicitly showing that they are unique maximizers of the likelihood function. (Hint: The function...
Q3. [10 points [Serial Correlation Consider a simple linear regression model with time series data: Suppose the error ut is strictly exogenous. That is Moreover, the error term follows an AR(1) serial correlation model. That where et are uncorrelated, and have a zero mean and constant variance a. 2 points Will the OLS estimator of P be unbiased? Why or why not? b. [3 points Will the conventional estimator of the variance of the OLS estimator be unbiased? Why or...