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| Question | Answer |
| Standardized random variable | A random variable x is a variable whose outcome is determined by chance |
| Statistic | A method or procedure to calculate a quantity from the sample |
| Sampling distribution | The sampling distribution of an estimate is the probability distribution over all possible outcomes |
| Population standard deviation | Is given by σ and measures the variance from the population mean |
| Probability Density Function | A probability density function f(x) is a non-negative function that describes a continuous random variable X. The area under the graph is probability |
| Hypothesis | Statement about a population parameter |
| Null hypothesis H0 | “status quo” – something you don’t expect = >= <= |
| Alternative Hypothesis HA | What you expect, change from status quo – what you’re trying to confirm /= < > |
| Regression Analysis | Technique to quantify a relation between 2 or more variables. Uses variation in one or more variables to explain/predict variation in another variable. Regression can only establish existence of a relation. But not whether the relation is causal |
| Stochastic Error Term | A term that is added to a regression equation to introduce all of the variation in Y that cannot be explained by the included X’s. |
| Ordinary Least Squares (OLS) | A regression estimation technique that calculates the β ̂s so as to minimize the sum of the squared residuals. |
| Multivariate Regression Coefficient | Indicates the change in the dependent variable associated with a one-unit increase in the independent variable in question holding constant the other independent variables in the equation. |
| Estimator | A statistic used to estimate a particular parameter |
| Estimate | A particular value determined by the estimators |
| 6 Steps to Hypothesis Testing | Step 1: Formulate null and alternate hypothesis Step 2: Set the significance level Step 3: Determine the critical value and rejection region of the test. The critical value z* or t* is such that a probability is in the “tails” Step 4: Calculate the statistic using sample information and H0 Step 5: Compare value of z or t to z* or t* - Reject H0 or fail to reject H0 Step 6: State the conclusions |
| Explain the difference between µ and X ̅. | µ is the population mean X ̅ is the sample mean |
| What is the difference between an estimator and an estimate? Give an example of each. | Estimator is a statistic used to estimate a particular parameter: OLS is an estimator Estimate is a particular value determined by the estimators: β ̂ produced by OLS is an estimate |
| Equation to Calculate Beta Hat 1 | |
| Equation to Calculate Beta Hat 0 | |
| TSS = RSS + ESS | Total Sum of Squares = Explained Sum of Squares + Residual Sum of Squares |
| R^2 represents what value? | coefficient of determination (ESS / TSS) or [1 - (RSS / TSS)] |
| Formula to Calculate R^2 | (ESS / TSS) or [1 - (RSS / TSS)] |
| Formula to Calculate Rbar^2 | |
| The Residual Value | |
| Total Sum of Squares | TSS = ESS + RSS |
| Explained Sum of Squares | Attributable to the fitted regression line |
| Residual Sum of Squares | The unexplained portion of TSS in an empirical sense by the estimated regression equation |
| The Simple Correlation Coefficient, r | A measure of the strength and direction of the linear relationship between two variables 1. If two variables are perfectly positively correlated, then r = +1 2. If two variables are perfectly negatively correlated, then r = -1 3. If two variables are totally uncorrelated, then r = 0 |
| Degrees of Freedom | The excess number of observations over the number of coefficients (N - 1) ------------- (N - K - 1) |
| R ̅^2 | Measures the percentage of the variation of Y around its mean that is explained by the regression equation, adjusted for degrees of freedom. |
| Unbiased Estimator | The estimator beta hat is an unbiased estimator if its expected value (taken with respect to its sampling distribution) is equal to the population parameters. In other words, E(Bhat) = B |
| Six steps of Applied Regression Analysis | |
| 3 components of specifying a model | 1) The independent variables and how they should be measured 2) the functional (mathematical) form of the variables 3) the properties of the stochastic error term |
| Specification Error | A mistake in any of the three elements of specification |
| dummy variable | A variable that takes on the value of 1 or 0 depending on whether a specified condition holds |
| Priors | prior theoretical beliefs, or working hypothesis, imposed on a regression equation |
| Outlier | An observation that lies outside the range of the rest of the observations. Looking for outliers is an easy way to find data entry errors |
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