Exam 4: Basic Estimation Techniques

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In the linear model Y=a+bX+cZY = a + b X + c Z , a test of the hypothesis that parameter c equals zero is

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D

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 exact level of significance of b^\hat { b } is

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C

The sample regression line

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B

In the nonlinear function Y=aXbZ2Y = a X ^ { b } Z ^ { 2 } , the parameter c measures

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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 -The estimated value of a is

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To test whether the overall regression equation is statistically significant one uses

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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 -Which of the parameter estimates are statistically significant at the 90% level of confidence?

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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 -The estimated value of a is

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Which of the following is an example of a time-series data set?

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Tests for statistical significance must be performed

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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}  -The value of R<sup>2</sup> indicates that _______ of the total variation in C is explained by the regression equation. 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 -The value of R2 indicates that _______ of the total variation in C is explained by the regression equation.

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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 20 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 20 units, what is average cost?

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In a linear regression equation Y = a + bX, the fitted or predicted value of Y is

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If an analyst believes that more than one explanatory variable explains the variation in the dependent variable, what model should be used?

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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 S increases by 8% (all other things constant), Y will

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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 -Hiring one more guard per week will decrease the losses due to theft at the warehouse by _________ per week.

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In a regression equation, the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables.

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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 -The nonlinear relation can be transformed into the following linear regression model:

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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 -The nonlinear relation can be transformed into the following linear regression model:

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A parameter estimate is said to be statistically significant if there is sufficient evidence that the

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