Exam 4: Basic Estimation Techniques

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In a linear regression equation of the form Y = a + bX, the intercept parameter a shows

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In a linear regression equation of the form Y = a + bX, the slope parameter b shows

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A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results: DEPENDENT VARIAELE: T R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 27 42.38 PARAMETER STANDARD VARIAELE ESTMATE ERROR T-RATIO P-VALUE INTERCEPT 5150.43 1740.72 G -480.92 130.65 - U 211.0 75.0 -Aone percent increase in the level of unemployment in the county results in an increase in losses due to theft of __________ more losses per week.

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Refer to the following computer output from estimating the parameters of the nonlinear model DEPENDENT VARIAELE: LNY R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 32 PARAMETER STANDARD VARIAELE ESTMATE ERROR T-RATIO P-VALUE INTEREEPT LNRR 1.36 LNS -1.83 LNT -If R = 1, S = 2, and T = 3, what value do you expect Y will have?

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Refer to the following nonlinear model which relates W to P, Q, and R: W=aPbQcRdW = a P ^ { b } Q ^ { c } R ^ { d } The computer output form the regression analysis is: DEPENDENTVARIAELE: LNW R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 19 43.12 PARAMETER STANDARD VARIAELE ESTMMATE ERROR T-RATIO P-VALUE INTERCEPT LNP -5.10 1.75 - LNQ 12.4 LNR 1.5 -400 -If P = Q = R = 1, what value do you expect W will have?

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Refer to the following nonlinear model which relates W to P, Q, and R: W=aPbQcRdW = a P ^ { b } Q ^ { c } R ^ { d } The computer output form the regression analysis is: DEPENDENTVARIAELE: LNW R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 19 43.12 PARAMETER STANDARD VARIAELE ESTMMATE ERROR T-RATIO P-VALUE INTERCEPT LNP -5.10 1.75 - LNQ 12.4 LNR 1.5 -400 -If R decreases by 12% (all other things constant), W will

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An estimator is unbiased if it produces

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Refer to the following computer output from estimating the parameters of the nonlinear model DEPENDENT VARIAELE: LNY R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 32 PARAMETER STANDARD VARIAELE ESTMATE ERROR T-RATIO P-VALUE INTEREEPT LNRR 1.36 LNS -1.83 LNT -If R decreases by 10% (all other things constant), Y will

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The critical value of t is the value that a t-statistic must exceed in order to

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Suppose you are testing the statistical significance (at the 1% significance level) of a parameter estimate from the estimated regression model: M = a + bR + cI Which is estimated using a cross-section data set on 22 firms. The critical value of the appropriate test statistic is

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Refer to the following nonlinear model which relates W to P, Q, and R: W=aPbQcRdW = a P ^ { b } Q ^ { c } R ^ { d } The computer output form the regression analysis is: DEPENDENTVARIAELE: LNW R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 19 43.12 PARAMETER STANDARD VARIAELE ESTMMATE ERROR T-RATIO P-VALUE INTERCEPT LNP -5.10 1.75 - LNQ 12.4 LNR 1.5 -400 -If P = 0.5, Q = 1.5, and R = 0.8, what value do you expect W will have?

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A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results: DEPENDENT VARIAELE: T R-SQUARE F-RATIO P-VALUE ONF OESERVATIONS: 27 42.38 PARAMETER STANDARD VARIAELE ESTMATE ERROR T-RATIO P-VALUE INTERCEPT 5150.43 1740.72 G -480.92 130.65 - U 211.0 75.0 -Which of the following is correct at the 1% level of significance?

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If the p-value is 10%, then the

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A manager wishes to estimate an average cost equation of the following form:    A manager wishes to estimate an average cost equation of the following form:     where Q is the level of output. Letting Z = Q<sup>2</sup> and using least-squares estimation, the manager obtains the following computer output:    \begin{array} { | c l l l l l | }  \hline \text { DEPENDENT VARIABLE: } & \text { C } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ON F } \\ \text { OBSERVATIONS: } & 28 & 0.7679 & 26.47 & 0.0001 & \\  \text { VARIABLE }  & \begin{array} { l }  \text { PARAMETER } \\ \text { ESTIMATE } \end{array} & \begin{array} { l }  \text { STANDARD } \\ \text { ERROR } \end{array}& \text { T-RATIO } & \text { P-VALUE } \\ \text { INTERCEPT }&  200 & 38.00 & 5.26 & 0.0001 \\ \text { Q }   & - 12.00 & 4.36 & - 2.75 & 0.0111 \\  \text { Z } & 0.50 & 0.16 & 3.13 & 0.0046 \\ \hline \end{array}  -Which of the parameter estimates are statistically significant at the 1% significance level? where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager obtains the following computer output: DEPENDENT VARIABLE: C R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 200 38.00 5.26 0.0001 Q -12.00 4.36 -2.75 0.0111 Z 0.50 0.16 3.13 0.0046 -Which of the parameter estimates are statistically significant at the 1% significance level?

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The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: Y R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 15.48 5.09 3.04 0.0008 X -21.36 8.03 -2.66 0.0171 -The parameter estimate of b indicates

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Suppose you are testing the statistical significance (at the 5% significance level) of a parameter estimate from the estimated regression equation: Y = a + bR + cS + dW Which is estimated using a time-series sample containing monthly observations over a 30-month time period. The critical value of the appropriate test statistic is

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The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: Y R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 15.48 5.09 3.04 0.0008 X -21.36 8.03 -2.66 0.0171 -The value of the R2 statistic indicates that

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The method of least squares

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A manager wishes to estimate an average cost equation of the following form:    A manager wishes to estimate an average cost equation of the following form:     where Q is the level of output. Letting Z = Q<sup>2</sup> and using least-squares estimation, the manager obtains the following computer output:    \begin{array} { | c l l l l l | }  \hline \text { DEPENDENT VARIABLE: } & \text { C } & \text { R-SQUARE } & \text { F-RATIO } & \text { P-VALUE ON F } \\ \text { OBSERVATIONS: } & 28 & 0.7679 & 26.47 & 0.0001 & \\  \text { VARIABLE }  & \begin{array} { l }  \text { PARAMETER } \\ \text { ESTIMATE } \end{array} & \begin{array} { l }  \text { STANDARD } \\ \text { ERROR } \end{array}& \text { T-RATIO } & \text { P-VALUE } \\ \text { INTERCEPT }&  200 & 38.00 & 5.26 & 0.0001 \\ \text { Q }   & - 12.00 & 4.36 & - 2.75 & 0.0111 \\  \text { Z } & 0.50 & 0.16 & 3.13 & 0.0046 \\ \hline \end{array}  -When output is 40 units, what is average cost? where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager obtains the following computer output: DEPENDENT VARIABLE: C R-SQUARE F-RATIO P-VALUE ON F OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 200 38.00 5.26 0.0001 Q -12.00 4.36 -2.75 0.0111 Z 0.50 0.16 3.13 0.0046 -When output is 40 units, what is average cost?

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The quadratic equation Y = a + bX +cX2 can be estimated using linear regression by estimating

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