Hello I have this econometrics question that I have to solve without computer.

(True model) yi = B0 + B1x1i + B2x2i + B3x3i + ui

(Regression model) ^yi = 13.16 - 0.052(x1i - x21) + 0.2x3i
SST = 1833
R^2 = known
R^2 (bar) = known
n = known

with the standard errors being respectively: (0.403) (0.121) (0.136)

I want to test the hypothesis that
H0: B1 = B2 = B3
alpha = 1%

Thank you for your help!

To test the hypothesis H0: B1 = B2 = B3, you can use the F-test.

The F-test compares the regression sum of squares (RSS) between the full model (with all the independent variables) and the restricted model (with the null hypothesis in place).

Here are the steps to perform the F-test to test the hypothesis:

Step 1: Calculate the residual sum of squares (RSS) for the restricted model.
To do this, you need to calculate the predicted values ^yi using the regression coefficients from the restricted model, and then calculate the residuals by subtracting the observed values yi from the predicted values ^yi. Next, square the residuals and sum them up to get the RSS_r.

Step 2: Calculate the residual sum of squares (RSS) for the full model.
Similarly, calculate the predicted values ^yi using the regression coefficients from the full model. Calculate the residuals by subtracting the observed values yi from the predicted values ^yi. Square the residuals and sum them up to get the RSS_f.

Step 3: Calculate the test statistic F.
The test statistic F can be calculated as:
F = [(RSS_r - RSS_f) / q] / [RSS_f / (n - k)]

Where:
- q is the number of restrictions (in this case, q = 3, because there are three independent variables being restricted).
- n is the sample size.
- k is the number of independent variables in the full model (including the intercept term).

Step 4: Calculate the critical value from the F-distribution.
Find the critical value for the desired significance level (alpha). Since alpha = 1%, the critical value will depend on the degrees of freedom degrees of freedom for the numerator (q) and degrees of freedom for the denominator (n - k).

Step 5: Compare the test statistic with the critical value.
If the test statistic is greater than the critical value, reject the null hypothesis (H0). Otherwise, fail to reject the null hypothesis.

Note: The F-test assumes that the errors are normally distributed and have constant variance.

Additionally, the information provided (such as SST, R^2, R^2(bar), and standard errors) does not seem to be directly relevant to performing the F-test for your hypothesis.