Key Terms
Standard Deviation (SD): A common measure of spread in the distribution of a random
variable
Standard Error of the Regression (SER): In multiple regression analysis, the estimate of the
SD of the population error, obtained as the square root of the sum of squared residuals over the
degrees of freedom.
̂𝒊 ): An estimate of the SD in the
Standard Error of Estimated coefficient (i.e. slope) (𝜷
sampling distribution of 𝛽̂𝑖 of the regression line.
̂𝟏 : The SE of the OLS slope estimator. In the simple regression model,
Standard Error of the 𝜷
̂1 ) =
this is SE(𝛽
̂
𝜎
√𝑆𝑆𝑇𝑥
Critical value: In hypothesis testing, the value against which a test statistic is compared to
determine whether or not the null hypothesis is rejected. In other words, the value of a test
statistic for which the test just rejects the null hypothesis at the given significance level.
Significance Level:
The probability of wrongly accepting the alternative hypothesis when the null hypothesis is
true (i.e. making type I error). It is based on the theoretical probability of the occurrence of rare
sample values that could have been produced using probability procedures. If the level set is
equalled or exceeded in the analysis, the sample difference is expected to be significant (i.e.
this value or difference is expected to be present in the population from which the sample was
drawn). Common significance levels are 5% (0.05), 1% (0.01), 0.1% (0.001).
Confidence Interval:
An interval (or set) that contains the true value of a population parameter with a pre-specified
probability when computed over repeated samples. It is also defined as the range of values
around the sample value within which the population value is expected to lie.
Confidence Level: The pre-specified probability that a confidence interval (or set) contains
the true value of the parameter.