Chapter 4: Basic Estimation Techniques

Question 1

Total cost (C)

Answer 1

C=a + bQ + cQ^2 + dQ^3
(C=total cost $)
(Q=quantity/output)
(a,b,c,d = parameters of the cost efficient)

Question 2

parameters

Answer 2

The coefficients in an equation that determine the exact mathematical relation among the variables. [true values]

Question 3

parameter estimation

Answer 3

The process of finding estimates of the numerical values of the parameters of an equation. [estimate ^]

Question 4

regression analysis

Answer 4

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

Question 5

dependent variable

Answer 5

The variable whose variation is to be explained.

Question 6

explanatory variables / independent variable

Answer 6

The variables that are thought to cause the dependent variable to take on different values.

Question 7

Simple Linear Regression

Answer 7

𝒀=𝒂+𝒃𝑿 (Y=mx+b); equation for a straight line

Question 8

intercept parameter (a)

Answer 8

The parameter that gives the value of Y at the point where the regression line crosses the Y-axis.

Question 9

slope parameter (b,m)

Answer 9

slope = ch Y/ch X 
(slope =  rise / run)

Question 10

random (stochastic) error term

Answer 10

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)

Question 11

time-series

Answer 11

A data collected over time for a SINGLE firm

Question 12

Cross-sectional

Answer 12

A data collected over time for a MANY different firms at a given time

Question 13

Scatter diagram

Answer 13

A graph of the data points in a sample.

Question 14

sample regression line

Answer 14

The line that best fits the scatter of data points in the sample and provides an estimate of the population regression line.

Question 15

population regression line

Answer 15

The equation/line representing the true (or actual) underlying relation between the dependent variable and the explanatory variable (true regression line)

Question 16

method of least squares

Answer 16

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.

Question 17

Estimators

Answer 17

the formulas by which the estimates of parameters are calculated

Question 18

Parameter estimates

Answer 18

obtained by substituting sample data into estimators (they are the values of a and b that minimize the sum of squared residuals)

Question 19

residual

Answer 19

the difference between the actual and fitted values of Y: Yi – Ŷi

Question 20

Statistical significance

Answer 20

There is sufficient evidence from the sample to indicate that the true value of the coefficient is not zero.

Question 21

Hypothesis testing

Answer 21

A statistical technique for making a probabilistic statement about the true value of a parameter

Question 22

unbiased estimator

Answer 22

an estimator that produces estimates of a parameter that are, on average, equal to the true value of the parameter.

Question 23

relative frequency distribution

Answer 23

The distribution (and relative frequency) of values b̂ can take because observations on Y and X come from a random sample.

Question 24

t-test

Answer 24

A statistical test used to test the hypothesis that the true value of a parameter is equal to 0 (b = 0).

Question 25

t-ratio / t-value / t-statistic

Answer 25

The ratio of an estimated regression parameter divided by the standard error of the estimate. [t=^b / S (^b)]

Question 26

level of significance

Answer 26

The probability of finding the parameter to be statistically significant when in fact it is not.

Question 27

level of confidence

Answer 27

The probability of correctly failing to reject the true hypothesis that b = 0; equals one minus the level of significance.

Question 28

degrees of freedom

Answer 28

The number of observations in the sample (n) minus the number of parameters being estimated by the regression analysis (k)

(n − k)

Question 29

purpose of regression analysis

Answer 29

1. estimate the parameters (a and b) of the true regression line
2. test whether the estimate values of the parameters are statistically significant

Question 30

fitted or predicted value

Answer 30

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.

Question 31

critical value of t

Answer 31

The value that the t-statistic must exceed in order to reject the hypothesis that b = 0

Question 32

type I error

Answer 32

Error in which a parameter estimate is found to be statistically significant when it is not.

Question 33

p-value

Answer 33

The exact level of significance for a test statistic, which is the probability of finding significance when none exists.

Question 34

coefficient of determination (R^2)

Answer 34

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

Question 35

multiple regression models

Answer 35

Regression models that use more than one explanatory variable to explain the variation in the dependent variable. [𝑌=𝑎+𝑏𝑋+𝑐𝑊+𝑑𝑍]

Question 36

quadratic regression model

Answer 36

A nonlinear regression model
Y = a + bX + cX^2
Y=a + bX + cZ, where Z=X^2

Question 37

log-linear regression model

Answer 37

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)

Question 38

F-statistic

Answer 38

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

Question 39

results of performing a t-test

Answer 39

if abs of t-statistic = | t | > critical t then b<>0/reject b=0 or b is statistically significant or significantly different from 0