Chapter 4 SB
The coefficient of determination can range from ______, which means the regression equation explains none of the variation in Y, to _____, which means that the regression equation explains all of the variation in Y.
0; 1
The level of confidence when the level of significance is 0.05 is
95% confidence.
_________ uses data on economic variables to determine a mathematical equation that describes the relationship between the economic variables
Regression analysis
________ is an example of a multiple regression equation
Y = a + bX + cW + dZ
A linear regression analysis estimates the parameters of the equation
Y = a + bx.
If the t-statistic is greater than the critical value of t, we say
b is statistically significant.
The slope parameter(s) in Y = a + bX + cW + dZ is(are)
b, c, and d.
A(n) _______ is a data set in which the data on the dependent and explanatory variables are collected from many different firms or industries at a given point in time.
cross-sectional data set
Hypothesis testing is a tool that
determines whether the coefficients are statistically different from 0 helps to determine if estimates are statistically significantmakes a probabilistic statement about the true value of a parameter
A regression equation shows the _______ level of a dependent variable given levels of explanatory variables.
expected
A(n) _______ variable affects the value of the _______ variable.
explanatory; dependent
A Type I error is
finding a parameter estimate significant when it is not.
If the t-statistic is ______ than the critical value of t, the hypothesis that b=0 is ______.
greater; rejected
The regression model expressed as Y = a + bX + cX2
has a ∩ shape if b is positive and c is negative. has a U shape if b is negative and c is positive. can be estimated as a linear regression model by replacing X2 with a new variable Z that is equal to X2. is an example of a non-linear regression model.
If the value of R2 is ______, there is high correlation between the dependent and independent variables.
high
In the equation Y = a + bx, a is the _______ parameter and b is the _______ parameter.
intercept; slope
The method of ________ is a method of estimating 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.
least squares
The equation Y = aXbZc is a _______ regression model.
log-linear
The coefficient of determination
measures the fraction of the total variation in the dependent variable that is explained by the regression equation.
The method of least squares finds the sample regression line that
minimizes the sum of the squared distances from each sample data point to the sample regression line.
A _______ allows two or more explanatory variables to explain the variation in the dependent variable.
multiple regression model
A ______ regression model is used when the underlying relation between Y and X plots as a curve, rather than a straight line.
nonlinear
A quadratic regression model is an example of a _______ regression model.
nonlinear
The _______ for an F-statistic gives the exact level of significance for the regression equation as a whole.
p-value
An unbiased estimator is an estimator that
produces estimates that are on average equal to the true parameter.
The ________ captures the effects of all the minor unpredictable factors that cannot reasonably be included in the model as explanatory variables.
random error term
The values of parameters are often obtained by using _________.
regression analysis
The _______ is the distribution of the values an estimate can take because the observations of the variables X and Y come from a random sample.
relative frequency distribution
When plotted on a graph, all data results in a ________.
scatter diagram
If an estimated coefficient is far enough away from 0, it is considered to be
statistically significant.
The t-ratio is
t = b / Sb
A p-value associated with a t-statistic gives
the exact level of significance for a t-ratio associated with a parameter estimate
The equation Y = aXbZc is often used in economics because
the parameter estimates b and c are elasticities.
The F-statistic from a regression estimate provides a measure of
the ratio of explained variation in the dependent variable.
The objective of regression analysis is to find
the straight line that best fits a scatter of data points. estimates of the true slope and intercept parameters.
Data collected over time is called a
time series
True or false: The least-squares estimator of a and b is an unbiased estimator.
true
True or false: The probability of drawing a sample for which the estimate of b is much larger than 0 is very small when the true value of b is actually 0.
true
A multiple regression model uses ______ explanatory variables
two or more
