LSUS MBA 740 | Exam 2 | STUDY GUIDE
a statistical technique that can be used to model the relationship
Regression analysis
between a dependent (outcome) variable and independent (predictor)
variables
simple regression predicting a metric outcome based on a single metric or nonmetric predictor
multiple regression predicting a metric outcome based on multiple metric and/or nonmetric predictors
logistic regression predicting a nonmetric outcome based on metric and/or nonmetric predictors
e or ϵ is the difference between the observed and predicted values of
prediction error (error term, residual)
the dependent variable
regression attempts to minimize the sum of the squared errors to
produce the best fitting line
least squares estimation
We use the sum of squared error rather than simply the sum of errors
because the sum of errors will always equal 0.
R^2 called? coefficient of determination
represents the proportion of variance accounted for by the regression
model. It tells how much better our model is compared to simply using
R^2 (coefficient of determination)
the mean.
A mean model has an R^2 of 0.
represents the average distance that observed values fall from the
regression line. A larger value indicates that observed values are
typically farther away from their predicted values. It gives us an idea of
the accuracy of our regression model's predictions.
Standard Error of the Estimate (SE_E)
SE_E lets us calculate the confidence interval and prediction interval for
our predictions.
SE_E = SQRT ( (sum of squared errors) / (sample size - 2))
, What is the purpose of calculating the SE_E lets us calculate the confidence interval and prediction interval for
standard error of the estimate (SE_E)? our predictions.
reflects the idea that if we were to take many samples and construct
confidence intervals in the same way from each sample, a certain
percentage (1 - alpha) of those intervals would contain the true parameter
value.
confidence interval
For example, for alpha 0.05, we can state that if we would repeat our
sampling process infinitely, 95% of the constructed confidence intervals
would contain the true population mean.
In other words, there is a 95% chance of selecting a sample such that
the 95% confidence interval calculated from that sample contains the
true population mean.
signifies greater precision in the estimate of the parameter but does
narrow confidence interval not necessarily guarantee accuracy—i.e., that the parameter estimate is
close to the true parameter value
an estimate of an interval in which a future observation will fall, with a
certain confidence level, given the observations that were already
observed.
prediction interval
At a 95% prediction interval we can state that if we would repeat our
sampling process infinitely, 95% of the constructed prediction intervals
would contain the new observation.
simple: Y = b0 + b1x1
simple regression vs. multiple regression
multiple: Y = b0 + b1x1 + b2x2
expands upon simple by adding independent variables
Explain why adding additional The addition of more independent variables is based on trade-offs
variables to a regression model can between increased predictive power versus overly complex and even
be counterproductive even when potentially misleading regression models.
they enhance the model's ability to
predict outcomes
The presence of multicollinearity makes it more difficult to identify
the true contribution of any single variable to the model's ability to
predict an outcome.
Explain the impact of
To maximize a model's predictive ability, we should look for
multicollinearity on the estimation
independent variables that have low multicollinearity with the other
of regression coefficients
independent variables but also have high correlations with the
dependent variable.
Remember that variables selected for inclusion in a model should
ideally be those that have high collinearity with the outcome but low
multicollinearity with each other
A functional relationship calculates an exact value, whereas a statistical
relationship estimates an average value because some random
Describe what distinguishes a component will always be present.
functional relationship from a statistical
relationship Multiple regression is appropriate when the objective is to examine a
statistical relationship as opposed to a functional relationship.
a statistical technique that can be used to model the relationship
Regression analysis
between a dependent (outcome) variable and independent (predictor)
variables
simple regression predicting a metric outcome based on a single metric or nonmetric predictor
multiple regression predicting a metric outcome based on multiple metric and/or nonmetric predictors
logistic regression predicting a nonmetric outcome based on metric and/or nonmetric predictors
e or ϵ is the difference between the observed and predicted values of
prediction error (error term, residual)
the dependent variable
regression attempts to minimize the sum of the squared errors to
produce the best fitting line
least squares estimation
We use the sum of squared error rather than simply the sum of errors
because the sum of errors will always equal 0.
R^2 called? coefficient of determination
represents the proportion of variance accounted for by the regression
model. It tells how much better our model is compared to simply using
R^2 (coefficient of determination)
the mean.
A mean model has an R^2 of 0.
represents the average distance that observed values fall from the
regression line. A larger value indicates that observed values are
typically farther away from their predicted values. It gives us an idea of
the accuracy of our regression model's predictions.
Standard Error of the Estimate (SE_E)
SE_E lets us calculate the confidence interval and prediction interval for
our predictions.
SE_E = SQRT ( (sum of squared errors) / (sample size - 2))
, What is the purpose of calculating the SE_E lets us calculate the confidence interval and prediction interval for
standard error of the estimate (SE_E)? our predictions.
reflects the idea that if we were to take many samples and construct
confidence intervals in the same way from each sample, a certain
percentage (1 - alpha) of those intervals would contain the true parameter
value.
confidence interval
For example, for alpha 0.05, we can state that if we would repeat our
sampling process infinitely, 95% of the constructed confidence intervals
would contain the true population mean.
In other words, there is a 95% chance of selecting a sample such that
the 95% confidence interval calculated from that sample contains the
true population mean.
signifies greater precision in the estimate of the parameter but does
narrow confidence interval not necessarily guarantee accuracy—i.e., that the parameter estimate is
close to the true parameter value
an estimate of an interval in which a future observation will fall, with a
certain confidence level, given the observations that were already
observed.
prediction interval
At a 95% prediction interval we can state that if we would repeat our
sampling process infinitely, 95% of the constructed prediction intervals
would contain the new observation.
simple: Y = b0 + b1x1
simple regression vs. multiple regression
multiple: Y = b0 + b1x1 + b2x2
expands upon simple by adding independent variables
Explain why adding additional The addition of more independent variables is based on trade-offs
variables to a regression model can between increased predictive power versus overly complex and even
be counterproductive even when potentially misleading regression models.
they enhance the model's ability to
predict outcomes
The presence of multicollinearity makes it more difficult to identify
the true contribution of any single variable to the model's ability to
predict an outcome.
Explain the impact of
To maximize a model's predictive ability, we should look for
multicollinearity on the estimation
independent variables that have low multicollinearity with the other
of regression coefficients
independent variables but also have high correlations with the
dependent variable.
Remember that variables selected for inclusion in a model should
ideally be those that have high collinearity with the outcome but low
multicollinearity with each other
A functional relationship calculates an exact value, whereas a statistical
relationship estimates an average value because some random
Describe what distinguishes a component will always be present.
functional relationship from a statistical
relationship Multiple regression is appropriate when the objective is to examine a
statistical relationship as opposed to a functional relationship.
