If we have the model: Y = Bo + B1X1 + B2X2 + B3X3 + B4X4 + e And we wish to test the usefulness of the whole model, what is the null hypothesis? O Ho : B1 = B2 = B3 = 0 O Ho : B1 = 0 O Ho : B1 = B2 = ß3 = B4 = 0 O Ho : B2 = B3 = 0
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- Explain the differences between Gaussian elimination and Gauss-Jordan elimination.What is the significance of R and R2 in gression model?In terms of the model parameters, state the null hypothesis that, after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases a CEO’s salary.
- If the data is highly skewed, can we still rely on the kurtosis coefficient? Why or why not?What would be my research hypothesis for this scenario?In the context of a controlled experiment, consider the simple linear regression formulation Yi = β0 + β1Xi + Ui. Let the Yi be the outcome, Xi the treatment level when the treatment is binary, and Ui contain all the additional determinants of the outcome. Then: a. the OLS estimator of the slope will be inconsistent in the case of a randomly assigned Xi since there are omitted variables present. b. Xi and Ui will not be independently distributed if the Xi are randomly assigned. c. β0 represents the causal effect of X on Y when X is zero. d. E(Y|X= 1) is the expected value for the treatment group. e. All of the above. f. None of the above.
- In a multiple linear regression model with 3 predictor variables, what is the t-statistic for the hypothesis test of the null hypothesis that the coefficient of the second predictor variable is equal to 0, if the estimated coefficient is 0.5, the standard error of the estimate is 0.1, and the degrees of freedom is 15?b) What are the three models proposed as extensions of the GARCH model? Describe their advantages over the GARCH.8)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.86, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
- The y-interept bo of a least-squares regression line has a useful interpretation only if the x-values are either all positive or all negative. Determine if the statement is true or false. Why? If the statement is false, rewrite as a true statement.9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5A set of paired data has a least squares regressionline with equation yn = 0.50x + 2.0 and a correlationcoefficient of r = 0.80. Suppose we convert the datafor each variable to z-scores and then compute the newregression line. What will the equation be?A) zˆy = 0.50zx B) zˆy = 0.64zxC) zˆy = 0.80zx D) zˆy = 0.50zx + 20E) zˆy = 0.80zx + 20