Chapter 4: Basic Estimation Techniques Flashcards
Total cost (C)
C=a + bQ + cQ^2 + dQ^3
(C=total cost $)
(Q=quantity/output)
(a,b,c,d = parameters of the cost efficient)
parameters
The coefficients in an equation that determine the exact mathematical relation among the variables. [true values]
parameter estimation
The process of finding estimates of the numerical values of the parameters of an equation. [estimate ^]
regression analysis
A statistical technique for estimating the parameters of an equation and testing for statistical significance. (AKA least square analysis) / uses data on economic variables to determine a mathematical equation that describes the relationship between the economic variables
dependent variable
The variable whose variation is to be explained.
explanatory variables / independent variable
The variables that are thought to cause the dependent variable to take on different values.
Simple Linear Regression
𝒀=𝒂+𝒃𝑿 (Y=mx+b); equation for a straight line
intercept parameter (a)
The parameter that gives the value of Y at the point where the regression line crosses the Y-axis.
slope parameter (b,m)
slope = ch Y/ch X (slope = rise / run)
random (stochastic) error term
An unobservable term added to a regression model to capture the effects of all the minor, unpredictable factors that affect Y but cannot reasonably be included as explanatory variables. (residual)
time-series
A data collected over time for a SINGLE firm
Cross-sectional
A data collected over time for a MANY different firms at a given time
Scatter diagram
A graph of the data points in a sample.
sample regression line
The line that best fits the scatter of data points in the sample and provides an estimate of the population regression line.
population regression line
The equation/line representing the true (or actual) underlying relation between the dependent variable and the explanatory variable (true regression line)
method of least squares
is a method of estimating the parameters of a linear regression equation by finding the line that minimizes the sum of the squared distances from each sample data point to the sample regression line.
Estimators
the formulas by which the estimates of parameters are calculated
Parameter estimates
obtained by substituting sample data into estimators (they are the values of a and b that minimize the sum of squared residuals)
residual
the difference between the actual and fitted values of Y: Yi – Ŷi
Statistical significance
There is sufficient evidence from the sample to indicate that the true value of the coefficient is not zero.
Hypothesis testing
A statistical technique for making a probabilistic statement about the true value of a parameter
unbiased estimator
an estimator that produces estimates of a parameter that are, on average, equal to the true value of the parameter.
relative frequency distribution
The distribution (and relative frequency) of values b̂ can take because observations on Y and X come from a random sample.
t-test
A statistical test used to test the hypothesis that the true value of a parameter is equal to 0 (b = 0).
t-ratio / t-value / t-statistic
The ratio of an estimated regression parameter divided by the standard error of the estimate. [t=^b / S (^b)]
level of significance
The probability of finding the parameter to be statistically significant when in fact it is not.
level of confidence
The probability of correctly failing to reject the true hypothesis that b = 0; equals one minus the level of significance.
degrees of freedom
The number of observations in the sample (n) minus the number of parameters being estimated by the regression analysis (k)
(n − k)
purpose of regression analysis
- estimate the parameters (a and b) of the true regression line
- test whether the estimate values of the parameters are statistically significant
fitted or predicted value
The predicted value of Y (denoted Ŷ) associated with a particular value of X, which is obtained by substituting that value of X into the sample regression equation.
critical value of t
The value that the t-statistic must exceed in order to reject the hypothesis that b = 0
type I error
Error in which a parameter estimate is found to be statistically significant when it is not.
p-value
The exact level of significance for a test statistic, which is the probability of finding significance when none exists.
coefficient of determination (R^2)
The fraction of total variation in the dependent variable explained by the regression equation; ranges from 0 and 1; closer it is to 1 the more correlated
multiple regression models
Regression models that use more than one explanatory variable to explain the variation in the dependent variable. [𝑌=𝑎+𝑏𝑋+𝑐𝑊+𝑑𝑍]
quadratic regression model
A nonlinear regression model
Y = a + bX + cX^2
Y=a + bX + cZ, where Z=X^2
log-linear regression model
A nonlinear regression model of the form Y = aX^bZ^c
𝑏= (Percentage change in 𝑌)/(Percentage change in 𝑋) 𝑐= (Percentage change in 𝑌)/(Percentage change in 𝑍)
𝑙𝑛𝑌=(𝑙𝑛𝑎)+𝑏(𝑙𝑛𝑋)+𝑐(𝑙𝑛𝑍)
F-statistic
A statistic used to test whether the overall regression equation is statistically significant; compare F-statistic to critical F-value from F-table; 2 degrees of freedom n-k & k-1
results of performing a t-test
if abs of t-statistic = | t | > critical t then b<>0/reject b=0 or b is statistically significant or significantly different from 0
