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Linear Regression - Now we can do inference (: testing etc)

Q: But suppose you'd like to test if the level of gov & lev are exactly the same h0=b1=b2 OR h0 is B1-B2=0

Then t-test is est beta's, subtract B-estimates (=0) and now you divide by the standard error of the difference of the beta hat. And remember the statistical rule, then the variance of b1hat-b2hat = var b1 + var b2 - s Covariance (b1 hat, b2hat) which is why we need the entire v-hat. so we've seen the t-test, testing 1 restriction. F-test is testing multiple restrictions at the same time

4 important questions on Linear Regression - Now we can do inference (: testing etc)

Now we come to the real goal, we would like to see if there's a relationship between y variable and certain x-variables so we discussed lots, latest were about assumptions that we needed to come up with a framework, distribution framework for beta hat and now given that we have this framework we can indeed test it/ do testing

Assumption 0a: correct specification
ob: no multicollinearity
1 zero mean errors
2 homoskedasticity
3 uncorrelated errors
regressors not stochastic
normality

Standard errors and t statistics
So then we'll end up with a framework and beta hat, is normally distributed. However, we estimate the variance so in the end t-dist. Take always estimated beta and you standardise it

Beta hat i - B i (value under h0)/St(=squareroot of V matrix(only diagonal of v matrix)) ~ T(0,1,N-K=df)

(if n is large, then normal dist) (at 2.5% one side higher than 1.9h)

T test is a test on one linear restriction

If test stat calc > 1.96 you reject the null hypothesis (or if < -1.96) cause then in rejection region. Cant reject H 0 in between. (if you assume a 5% significance level).

But suppose you'd like to test if the level of gov & lev are exactly the same
h0=b1=b2 OR h0 is B1-B2=0

Then t-test is est beta's, subtract B-estimates (=0) and now you divide by the standard error of the difference of the beta hat. And remember the statistical rule, then the variance of b1hat-b2hat = var b1 + var b2 - s Covariance (b1 hat, b2hat)
which is why we need the entire v-hat.

so we've seen the t-test, testing 1 restriction. F-test is testing multiple restrictions at the same time

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Linear Regression

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Linear Regression - Now we can do inference (: testing etc)

4 important questions on Linear Regression - Now we can do inference (: testing etc)

Standard errors and t statisticsSo then we'll end up with a framework and beta hat, is normally distributed. However, we estimate the variance so in the end t-dist. Take always estimated beta and you standardise it

T test is a test on one linear restriction

But suppose you'd like to test if the level of gov & lev are exactly the same h0=b1=b2 OR h0 is B1-B2=0

Summaries related to Linear Regression - transformations of variables (log-y instead of y, log-x instead of x)