Use the data in MEAP00 to answer this question. Estimate the model by OLS, and report...
Use the data in MEAP00 to answer this question.
-
Estimate the model
by OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5% level?
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Obtain the fitted values from the regression in part (i). What is the range of fitted values? How does it compare with the range of the actual data on math4?
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Obtain the residuals from the regression in part (i). What is the building code of the school that has the largest (positive) residual? Provide an interpretation of this residual.
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Add quadratics of all explanatory variables to the equation, and test them for joint significance. Would you leave them in the model?
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Returning to the model in part (i), divide the dependent variable and each explanatory variable by its sample standard deviation, and rerun the regression. (Include an intercept unless you also first subtract the mean from each variable.) In terms of standard deviation units, which explanatory variable has the largest effect on the math pass rate?
Homework Answers
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Use the data in MEAP00 to answer this question.
Estimate the model
by OLS, and report...
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 s...
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...
Question 4 3 pts Consider the estimated multiple regression model using OLS, with the standard errors...
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...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: spurious regression. omitted variable bias. multicollinearity. serial correlation.
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: omitted variable bias. o serial correlation. spurious regression. o multicollinearity.
Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very...
Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: multicollinearity. spurious regression. omitted variable bias. serial correlation.
3. In the multiple regression model shown in the previous question, which one of the following st...
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...
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)...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: O multicollinearity. omitted variable bias. O serial correlation. spurious regression. 3 pts Question 9
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the...
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the explanatory variables must be variable, non- stochastic and fixed in repeated samples. Under the conditions of perfect multicollinearity, the OLS estimators are not unique. The presence of heteroskedasticity causes the OLS method to overestimate the variances 2. 3. of the parameters. The Breusch-Godfrey LM test is applicable when a lagged dependent variable is used. If we include a non-influential variable in an equation the...
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently...
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be biased. the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients...
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...
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...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: spurious regression. omitted variable bias. multicollinearity. serial correlation.
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: omitted variable bias. o serial correlation. spurious regression. o multicollinearity.
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...
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)...
Question 8 3 pts Suppose you estimate a multiple regression model using OLS and the coefficient of determination is very high (above 0.8), while none of the estimated coefficients are (individually) statistically different from zero at the 5-percent level of significance. The most likely reason for this result is: O multicollinearity. omitted variable bias. O serial correlation. spurious regression. 3 pts Question 9
Answer each question by writing TRUE or FALSE 1. For OLS estimators to be linear the explanatory variables must be variable, non- stochastic and fixed in repeated samples. Under the conditions of perfect multicollinearity, the OLS estimators are not unique. The presence of heteroskedasticity causes the OLS method to overestimate the variances 2. 3. of the parameters. The Breusch-Godfrey LM test is applicable when a lagged dependent variable is used. If we include a non-influential variable in an equation the...
Question 14 3 pts Suppose that you estimate a multiple regression model, but that you inadvertently omit an explanatory variable that is correlated with the dependent variable. In this case, the coefficients on the included variables will always be biased. the coefficients on the included variables will always be unbiased, but the standard errors and test statistics will be biased. there is no effect on the coefficients of the included variables since the omitted variable has been omitted. the coefficients...
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