Question

In: Statistics and Probability

In a multivariate regression like Yi = α + β1X1i + β2X2i + β3X3i + i...

In a multivariate regression like Yi = α + β1X1i + β2X2i + β3X3i + i , explain how do we test the following three null hypothesis: H1 : β2 = 0, H2 : β3 = β2, and H3 : β1 = β2 = β3 = 0 (do not forget the name of the test and distribution under the null)

Solutions

Expert Solution

1) H1 : β2 = 0,

To test this hypothesis we use t-test

under H0

t-statistic= /SE()

The t-statistic has n – k – 1 degrees of freedom where k = number of independents variable here it is 3

The calculated value of this test statistic is compared to a critical value from the t-(df= n – k – 1) distribution.

If calculated value > a critical value we reject H0

====================================================

2) H2 : β3 = β2

To test this hypothesis we use t-test

under H0

t-statistic= (-)/(SE()^2 +SE()^2)

The t-statistic has n – k – 1 degrees of freedom where k = number of independents variable here it is 3

The calculated value of this test statistic is compared to a critical value from the t-(df= n – k – 1) distribution.

If calculated value > a critical value we reject H0

====================================================

3) H3 : β1 = β2 = β3 = 0

To test this hypothesis we use F-test

through this we test overall significance of model

F=(SST-SSE)/k-1/(SSE/(T-K))

The calculated value of this test statistic is compared to a critical value from the F(K-1,T-K) distribution.

If calculated value > a critical value we reject H0


Related Solutions

How can I explain multivariate regression?
How can I explain multivariate regression?
Formula that you might use: For a simple linear regression model yi= α + βxi+ui, i=1,2,...,N....
Formula that you might use: For a simple linear regression model yi= α + βxi+ui, i=1,2,...,N. Homework Assignment 1 1. Suppose researchers want to know the effect of elementary school class size on students’ math scores(total score is 100), intuitively they think there exists a negative linear relationship between class size and students’ math scores. The researchers want to know the marginal effect of class size on student’s math scores. 1) Based on the background information, design an linear regression...
If I ran a multivariate regression analysis for the effect of independent variables X and Y...
If I ran a multivariate regression analysis for the effect of independent variables X and Y on dependent variable A, that produced an adjusted R^2 of .0553, then added the independent variable Z to the analysis and got an adjusted R^2 of .0550, would that decrease in the adjusted R^2 translate to the independent variable Z not being a strong predictor of the dependent variable A? If it were a strong predictor of A would the adjusted R^2 increase?
Consider the following regression model: Yi = αXi + Ui , i = 1, .., n...
Consider the following regression model: Yi = αXi + Ui , i = 1, .., n (2) The error terms Ui are independently and identically distributed with E[Ui |X] = 0 and V[Ui |X] = σ^2 . 1. Write down the objective function of the method of least squares. 2. Write down the first order condition and derive the OLS estimator αˆ. Suppose model (2) is estimated, although the (true) population regression model corresponds to: Yi = β0 + β1Xi...
Consider the following (generic) population regression model: Yi = β0 + β1X1,i + β2X2,i + ui,=...
Consider the following (generic) population regression model: Yi = β0 + β1X1,i + β2X2,i + ui,= (∗) transform the regression so that you can use a t-statistic to test a. β1 = β2 b. β1 + 2β2 = 0. c. β1 + β2 = 1. (Hint: You must redefine the dependent variable in the regression.)
(i) Consider a simple linear regression yi = β0 + β1xi + ui Write down the...
(i) Consider a simple linear regression yi = β0 + β1xi + ui Write down the formula for the estimated standard error of the OLS estimator and the formula for the White heteroskedasticity-robust standard error on the estimated coefficient bβ1. (ii) What is the intuition for the White test for heteroskedasticity? (You do not need to describe how the test is implemented in practice.)
Following is a simple linear regression model: yi = /alpha + /beta xi + /epsilon i...
Following is a simple linear regression model: yi = /alpha + /beta xi + /epsilon i The following results were obtained from some statistical software. R2 = 0.735 syx (regression standard error) = 5.137 n (total observations) = 60 Significance level = 0.05 = 5% Variable Parameter Estimate Std. Err. of Parameter Est. Interecpt 0.325 0.097 Slope of X -1.263 0.309 1. Write the fitted model. (I ALREADY KNOW THE ANSWER TO THIS. I LEFT IT INCASE IT IS NEEDED...
3. Consider the simple linear regression Yi = 2Xi + ui for i = 1, 2,...
3. Consider the simple linear regression Yi = 2Xi + ui for i = 1, 2, . . . ,n. The ui are IID (0; 2 ). a. Derive OLS estimator of 2 and called it b 2 b. Find its variance c. Is b 2 unbiased, show it? d.What is the risk we run when we do not include an intercept in the regression? Do question d.
There are two OLS regression specification Yi = aSexi + ui (1) Yi = b Malei...
There are two OLS regression specification Yi = aSexi + ui (1) Yi = b Malei + c Femalei + ui(2) a, b, c, are constants. Sexi = 1 if the person is Female, and 0 otherwise. Malei = 1 if Sexi = 0, Femalei = 1 if Sexi = 1, and both are 0 otherwise. Why are neither regression(1) nor regression(2) directly tell you if the difference in Yi between Males and Females is statistically significant? What would be...
1. Why is a multivariate regression model usually better to use than a univariate regression model?...
1. Why is a multivariate regression model usually better to use than a univariate regression model? Define both and discuss at least two reasons.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT