Regression with a Single Regressor Hypothesis - Financial Risk Manager Video Lecture | Risk Management: An Essential Training - Management

simply learn your pace your place
financial risk manager frm part 1 of the
frm exam covers of fundamental tools and
techniques used in risk management and
the theories that underlie their use
hypothesis testing one regressor in the
previous slide we have learned the
basics of regression analysis of two
variables we've determined the
coefficients of the linear equation
showing the linear relationship between
the variables in this session we will
learn to test if the coefficients are
significantly different from the
hypothesized value under the given level
of confidence later
we'll learn testing of parameters in a
multiple regression analysis agenda
we'll begin our session from the
confidence interval for the coefficients
of the linear regression model these
confidence intervals will be based on
the given level of confidence we will
use these confidence intervals to test
if the hypothesized value is
significantly different from the actual
value we will use the t-test to test the
significance we will then learn about
heteroscedasticity which is one of the
violations of the assumptions in a
regression analysis where the variance
of the error terms is not constant we
will end the session by learning about
the gauss-markov theorem which lists the
properties of the ordinary least squares
estimators when the assumptions of the
regression model are true
confidence intervals from what we
learned in the previous sessions we know
that any confidence interval can be
obtained by adding or subtracting the
product of the reliability factor and
the standard error with the point
estimate the reliability factor is
usually the critical Z or T values for
the given confidence probability let us
find the confidence interval for the
regression coefficient b1 in this case
the point estimate of the coefficient B
1 is added to the product of the
critical T value and the standard error
of regression coefficient to get the
upper limit of the interval if it is a
two-tailed test then we also need to
subtract this from the point estimate to
get the lower limit in this case the
reliability factor or critical T value
is the value for a two-tailed test in
both cases the T value is 4 n minus 2
degrees of freedom because we have
estimated two values in the calculation
of b1 similarly we have the confidence
interval for the forecasted value of the