|addend||numbers you add together.|
|difference||answer to a subtraction sentence.|
|sum||answer to an addition sentence.|
|how many more||subtraction.|
|how many in all||add.|
|doubles facts||adding addends that the same 2 + 2|
|near doubles||adding an addend to a second addend that is one more in value example: 2 + 3|
|communicative property of addition||you can add numbers in any order.|
|>||is greater than.|
|is less than.|
|=||means equal or same.|
|9 + 9 = ?||Doubles|
|9 + 2 = ?||Counting On or Making Ten|
|6 + 5 = ?||Near Doubles|
|4 + 1 = ?||Counting On|
|7 + 6 = ?||Near Doubles|
|12 + 2 = ?||Counting On|
|4 + 3 = ?||Near Doubles or Counting On|
|8 + 7 = ?||Near Doubles|
|15 + 1 = ?||Counting On|
|2 + 3 = ?||Near Doubles or Counting On|
|11 + 2 = ?||Counting On or Making Ten|
|3 + 8 = ?||Making Ten or Counting On|
|4 + 9 = ?||Making Ten|
|12 + 9 = ?||Making Ten (or Making Twenty)|
|5 + 4 = ?||Near Doubles|
|6 + 6 = ?||Doubles|
|2 + 7 = ?||Counting On|
|8 + 9 = ?||Near Doubles|
|7 + 4 = ?||Making Ten or Counting On|
|3 + 5 = ?||Counting On|
|11 + 2 = ?||Counting On|
|7 + 7 = ?||Doubles|
|16 + 3 = ?||Counting On|
|8 + 3 = ?||Making Ten or Counting On|
|12 + 2 = ?||Counting On or Making Ten|
|5 + 6 = ?||Near Doubles|
|2 + 2 = ?||Doubles|
|7 + 1 = ?||Counting On|
|3 + 8 = ?||Making Ten or Counting On|
|Which classical assumption(s) does an Omitted Variable violate?||Violates Classical Assumptions I and III|
|What are the consequences of an Omitted Variable?||1) Estimated coefficient doesn’t equal actual coefficient.
2) Bias is forced onto another coefficient, causing the estimated value of the coefficient to change.
3) Increases by decreasing variance.
|What factors may indicate Omitted Variable bias?||1) Unexpected signs on the coefficient.
2) Too big of coefficients (if positive bias on a positive coefficient).
|How do you solve the problem of Omitted Variable bias?||Add omitted variable or proxy variable.|
|Which classical assumption(s) does a Redundant Variable violate?||Violates Classical Assumption VI|
|What are the consequences of a Redundant Variable?||1) Does NOT introduce bias.
2) Increases variance.
|How do you detect a Redundant Variable bias?||1) Decreased R2.
2) Wald Test.
|How do you solve the problem of Redundant Variable bias?||Drop irrelevant variable|
|How do you use to decide whether to include Omitted or Redundant Variables?||1) Theory.
3) Adjusted R2 decreases if the improvement in overall fit due to addition of the independent variables to the regression does NOT outweigh loss in degrees of freedom.
|Which classical assumption(s) does omitting an Intercept violate?||Violates Classical Assumption II: the error term has a zero population mean.
Intercept usually absorbs error.
|Which classical assumption(s) does Multicollinearity violate?||Violates Classical Assumption VI|
|What are the consequences of Multicollinearity?||1) Does not cause bias
2) MIGHT CAUSE WRONG SIGN DUE TO INCREASED VARIANCE
3) Increases variance because it impacts r sub1,2
4) T-scores Fall because SE increases
5) Will not fall much
|How do you detect Multicollinearity?||1) High Adjusted R2 and low t-scores.
2) High simple correlation coefficients (r sub1,2).
3) High Variance Inflation Factor (VIF > 5).
|How do you interpret VIF?||When VIF = 5, this means you have 5 times the variance in the model than you would have without the multicollinearity.|
|How do you solve the problem of Multicollinearity?||1) Do nothing
2) Drop variables
3) Transform variables
4) Increase sample size
|Which classical assumption(s) does Serial Correlation violate?||Violation of Classical Assumption IV|
|What are the consequences of Serial Correlation?||1) No bias in coefficient estimates.
2) TRUE Increased variance in coefficient estimates.
3) Distorts SEE portion of SE.
4) OLS no longer BLUE.
5) OLS underestimates standard error of the coefficients.
|How do you detect Serial Correlation?||1) T-scores appear larger than they really are, leading to Type I error
More likely to make a Type I error (reject a null hypothesis that is true)
2) Durbin-Watson test
|How do you solve the problem of Serial Correlation?||1) Better Specification
2) Generalized Least Squares
|Which classical assumption(s) does Heteroskedacity violate?||Violation of Classical Assumption V
Most common with cross-sectional models
|What are the consequences of Heteroskedacity?||1) No bias in coefficient estimates, t-scores are larger.
2) TRUE Increased variance in coefficient estimates
3) Distorts SEE portion of SE
4) OLS is no longer BLUE
5) OLS underestimates standard error of the coefficients.
|How do you detect Heteroskedacity?||1) Plot residuals to see if variance is constant. If bell or flower shape emerges, there is heteroskedasticity.
2) Park Test (for proportionality)
3) White Test
|How do you solve the problem of Heteroskedacity?||1) Weighted Least Squares.
2) Redefinition of Variables.
3) Heteroskedasticity Corrected Standard Errors.
|What is the basic idea of GLS?||1) Find rho by regressing lagged residuals against original residuals
2) Correct for serial correlation by subtracting lagged variables from original variables (and subtract rho from one on intercept) to remove serial correlation out of the equation.
|What are the 3 requirements to use DW test?||1) Must have an intercept
2) Cannot have lag regressors
3) Must be 1st order serial correlation
|How do you use the DW test? (3)||1) Null is that serial correlation exists
2) DW range is 0-4; 0 = extreme serial correlation
3) benchmark is 2 (if DW is greater than 2, no serial correlation)
• if DW is < dL, serial correlation exists
• if DW > dU, no serial correlation exists
|What are the 2 steps in the Park Test?||1) If you know Z factor, run regression of lnZ as independent variable and lne2 as dependent variable
2) Test significance of Z coefficient
– if significant, you know that Z is the cause of the heteroskedasticity
|What are the 2 steps in the White Test?||1) Runs regression of the square and product of all variables against square of residuals
2) Test overall significance with chi-squared test (N* )
– If chi test is significant, there is heteroskedasticity
– White can detect heteroskedasticity, but can'
|What is a benefit of the White Test?||Can also test for complex heteroskedasticity|
|perpendicular from centre to chord||the line drawn from the centre of a circle perpendicular to a chord bisects the chord|
|line from the centre to mid-point chord||the line drawn from the centre of the circle to the midpoint of a chord is perpendicular to the chord|
|perpendicular bisector of chord||the perpendicular bisector of a chord of a circle passes through the centre of the circle|
|Probability Distribution||provides probabilities for the possible values of a random variable; summarized by measures of the center (mean) and the spread (standard deviation)|
|Random Variable||a numerical measurement of the outcome of a random event|
|Expected Value||the mean of a probability distribution for a discrete random variable|
|Normal Distribution||the probability distribution of a continuous random variable that has a symmetric bell-shaped graph specified by mean and standard deviation|
|Standard Normal Distribution||it is the distribution of normal z-scores; the normal distribution with a mean = 0 and standard deviation = 1|
|Binary Data||data that has one of two possible outcomes|
|Binomial Distribution||the probability distribution of the discrete random variable that measures the number of successes X in n independent trials with the probability p of a success on a given trial.|
|Sampling Distribution||the probability distribution of a sample statistic; specifies the probabilities for the values of the statistic for all possible random samples|
|Sampling Distribution of the Mean||centered at the population mean|
|Standard Error||the standard deviation that describes the spread of the sampling distribution of the sample mean|
|×òî íàçûâàåòñÿ êîðíåì óðàâíåíèÿ?||Êîðíåì óðàâíåíèÿ íàçûâàåòñÿ çíà÷åíèå ïåðåìåííîé, ïðè êîòîðîì óðàâíåíèå îáðàùàåòñÿ â âåðíîå ðàâåíñòâî.|
|ßâëÿåòñÿ ëè ÷èñëî 2 êîðíåì óðàâíåíèÿ 5x-4=7?||Íåò|
|×òî çíà÷èò ðåøèòü óðàâíåíèå?||Ðåøèòü óðàâíåíèå – çíà÷èò íàéòè âñå åãî êîðíè èëè äîêàçàòü, ÷òî êîðíåé íåò.|
|Êàêèå óðàâíåíèÿ íàçûâàþòñÿ ðàâíîñèëüíûìè?||Äâà óðàâíåíèÿ íàçûâàþòñÿ ðàâíîñèëüíûìè, åñëè ìíîæåñòâà èõ êîðíåé ñîâïàäàþò.|
|Êàêîå óðàâíåíèå íàçûâàåòñÿ ëèíåéíûì óðàâíåíèåì ñ îäíîé ïåðåìåííîé?||Ëèíåéíûì óðàâíåíèåì ñ îäíîé ïåðåìåííîé íàçûâàåòñÿ óðàâíåíèå âèäà ax+b=c, ãäå x – ïåðåìåííàÿ, a, b, c – íåêîòîðûå ÷èñëà.|
|Ñêîëüêî êîðíåé ìîæåò èìåòü ëèíåéíîå óðàâíåíèå?||Îäèí, íè îäíîãî èëè ìíîæåñòâî êîðíåé.|
|absolute value||The distance a number is from zero on a number line.|
|integer||The set of numbers containing zero, the natural numbers, and all of the negatives of the natural numbers.|
|inverse operation||The operation that reverses the effect of another operation. Example: add and subtract or multiply and divide.|
|evaluate||To find the value of a numerical or algebraic expression.|
|explain||To make clear by describing it in more detail by providing more facts or ideas.|
|expression||Contains variables, numbers, and operations. It does not contain and equal sign.|
|equation||A mathematical sentence that shows two expressions are equal.|
|Order of Operations||Order of Operations: A rule for evaluating expressions. PEMDAS: Parenthesis, Exponents, Multiply/Divide, Add/Subtract.|
|Solution||A number that makes an equation true when it is substituted for the variable.|
|Associative Property||It does not matter how terms are grouped if they are added or multiplied the solution will be the same. Example: (3 + 4) + 5 = 3 + (4 + 5)|
|Commutative Property||It does not matter how terms are ordered if they are added or multiplied the solution will be the same. Example: 3 + 4 + 5 = 5 + 3 + 4|
|Distributive Property||If a term outside of the parenthesis is multiplied by terms inside parenthesis, the term can be multiplied by each term separately, then combined within the parenthesis. Example: 3( 4 + 5) = (3×4) + (3 x5)|
|isolate||To set apart from others.|
|Exponential Form||A number written using exponents|
|Expanded Form||A representation of a number in terms of powers of a base|
|exponential notation||show repeated multiplication by the same factor||5*5*5|
|base number||number to which one or more other numbers are appended or added by applying a table or other add or divide like instructions|