Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer. The OLS Sample regression equation passes through the point of sample mean
Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer.
i) The OLS Sample regression equation passes through the point of sample means
ii) The sum of the estimated () equals the sum of the observed ; or the sample mean of the estimated () equals the sample mean of the observed .
iii) The OLS residuals (i = 1, …, N) are uncorrelated with the estimated values of , the values (i = 1, …, N)
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Consider the following regression equation with the ususal assumptions of the Linear Regression Model. State whether the following are True or False. Give reasons for your answer. The OLS Sample regression equation passes through the point of sample mean
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State whether the following statements are correct or not in the context of regression analysis, and explain why: a. The sum of OLS residuals is zero. b. The OLS estimator of b0 of the regression equation y = b0 + u is the sample mean of y.
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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...
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Select all of the following statements that are true about linear regression analysis of quantitative variables. If the purpose of our regression model is prediction, it does not matter which variables we define as the explanatory and response variable. The observed values of Y will fall on the estimated regression line, while the predicted values of Y will vary around the regression line. The purpose of linear regression is to investigate if there exists a linear relationship between a response...
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Decide (with short explanations) whether the following
statements are true or false.
e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that homoskedasticity does not hold. Mathematically, this is expressed as In other words, the subscript i in σ12 means that the conditional variance of errors for each individual i is different. Under heteroskedasticity, we can derive the expression for the variance of Var(B) as SST Where SSTx is the...
(1) True or False: Please specify your reasons. (i) An estimator is unbiased, if its expected...
(1) True or False: Please specify your reasons. (i) An estimator is unbiased, if its expected value across different samples equals to the true value of the parameter. (ii) OLS estimator is always unbiased. (iii) We can use n- i-, û to estimate the error variance o2 because it is unbiased. (iv) If the sample size increases, we can have a better estimates of sd(Bo) and sd(B1).
Need help with stats true or false questions Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% con...
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
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Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
Question 4 3 pts Consider the estimated multiple regression model using OLS, with the standard errors in parentheses below each estimated coefficient. There are 1,576 observations in the sample: Y = 10 + 2X2i - 5Xzi (3) (1.5) (2) Suppose that the sample mean of Y is 30. For the 18th observation (i=18) in the sample, the value of X2 is 50, the value of X3 is 16, and the value of Y is 20. The residual associated with the...
Select all of the following statements that are true about linear regression analysis of quantitative variables. If the purpose of our regression model is prediction, it does not matter which variables we define as the explanatory and response variable. The observed values of Y will fall on the estimated regression line, while the predicted values of Y will vary around the regression line. The purpose of linear regression is to investigate if there exists a linear relationship between a response...
Decide (with short explanations) whether the following
statements are true or false.
e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statisties z-10, s/-3 sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f A standard multiple regression model with continuous predictors and r2, a categorical predictor T with four values, an interaction between a and...
Consider the following simple regression model: a. Suppose that OLS assumptions 1 to 4 hold true. We know that homoskedasticity assumption is statedas: Var[UjIx] = σ2 for all i Now, suppose that homoskedasticity does not hold. Mathematically, this is expressed as In other words, the subscript i in σ12 means that the conditional variance of errors for each individual i is different. Under heteroskedasticity, we can derive the expression for the variance of Var(B) as SST Where SSTx is the...
(1) True or False: Please specify your reasons. (i) An estimator is unbiased, if its expected value across different samples equals to the true value of the parameter. (ii) OLS estimator is always unbiased. (iii) We can use n- i-, û to estimate the error variance o2 because it is unbiased. (iv) If the sample size increases, we can have a better estimates of sd(Bo) and sd(B1).
Need help with stats true or false questions
Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c)...
Consider the multiple linear regression (MLR) model that satisfies the classical assumptions: Yi = Bo + B1Xil +...+Bkxik + Ui estimated by OLS/MOM. Let the estimators beßo, Ŝ1,..., ØK. Question 1 (1 point) The p-value for undertaking a hypothesis test is the smallest significance level for which we reject a null hypothesis that is correct. True False Question 2 (1 point) To test Ho: B3 = 34 vs H1 : B3 – B4 > 0, we form the test statistic...
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