Consider the following bivariate linear regression model y = a + Br + u. Suppose that Cov(x, u) > 0, Cov(z,x) > 0, and Cov(z, u) = 0. Then, plim(3oLs) > B and plim(ßrv) > plim(3oLs). O True O False
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A: Solution: According to the guidelines first question should be answered since the multiple questions…
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A: We know, Slope=∑ xy-1n∑ x∑ y∑ x2-1n∑ x2 =1687.9-115×53×582167.42-115×532 =18.567
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Q: The Simple Linear Regression model is Y = b0 + b1*X1 + u
A: According to guidelines we solve only first question when given questions are different.
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Q: QUESTION 28 Suppose your estimated MLR model is: Y_hat = -30 + 2*X1 + 10*X2 Suppose the standard…
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Q: The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression…
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Q: The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear…
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- Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.The ordered pairs below give the median sales prices y (in thousands of dollars) of new homes sold in a neighborhood from 2009 through 2016. (2009, 179.4) (2011, 191.0) (2013, 202.6) (2015, 214.9) (2010, 185.4) (2012, 196.7) (2014, 208.7) (2016, 221.4) A linear model that approximates the data is y=5.96t+125.5,9t16, where t represents the year, with t=9 corresponding to 2009. Plot the actual data and the model on the same graph. How closely does the model represent the data?Find the least squares regression line for the data points. (Let x be the independent variable and y be the dependent varia (-1, 1), (1, -1), (3,-2) 2 X
- ASAPThe Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 22 Suppose your estimated MLR model with two explanatory variables, X1 and log(X2), is: log(Y)_hat= 10 +0.5*X1 + 0.25*log(X2) Which of the following statements about the interpretation of the coefficient of log(X2) is correct? If X2 increases by 1%, Y is predicted to increase by approximately 25 units, holding X1 constant If X2 increases by 1%, Y is predicted to increase by approximately 0.25%, holding X1 constant If X2 increases by 1 unit, Y is…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 28 Suppose your estimated MLR model is: Y_hat = -30 + 2*X1 + 10*X2 Suppose the standard error for the estimated coefficient associated with X2 is equal to 5. Now, suppose that for some reason we multiply X2 by 5 and we re-estimate the model using the rescaled explanatory variable. What will be the value of the estimated coefficient of X2 and its standard error? The estimated coefficient of X2 will be equal to 50 and its standard error will be…
- The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 4 Suppose we have an SLR model, where the dependent variable (Y) represents ‘how satisfied someone is with his/her life, from 0 to 100’ (the higher the value, the higher the satisfaction with life), and the explanatory variable (X1) represents ‘personal annual income in £1,000’. The estimated OLS regression line is: Yhat = 33.2 + 0.74*X1. According to this model, what is the predicted life satisfaction, for someone with…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 1 In the SLR model, suppose the dependent variable (Y) represents the quantity consumed of apples in a particular area in tones, and the explanatory variable (X1) is the average price of apples in that area in £. If this model is estimated by OLS, then the estimated slope b1_hat, represents: by how many tones consumption of apples will change, if the average price of apples increases by £1 the predicted change in the consumption of apples (in…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if: one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) ) QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity'…
- The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5% QUESTION 17 In an MLR…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 13 In the MLR model, what do we mean by Heteroskedasticity? That the error term depends on the values of the explanatory variables That all the explanatory variables have different variance That the variance of the error term is a function of the explanatory variables That the variance of the error term is constant QUESTION 14 Suppose that in the model Y=b0+b1*X1+u, we add a variable that is correlated with both Y and X1. What will happen…The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 25 In the MLR model, with 150 observations and 5 explanatory variables, suppose you want to test the null hypothesis, H0: b3=0, b4=0 We also know that the RSS of the unrestricted model is 563, while the RSS of a model that excludes the variables associated with the 2 coefficients under the null hypothesis is 577. Given this information what is the F-statistic for this hypothesis? It is around -1.79 It is around 1.75 It is around -1.75 It is…
