Instruction 16-3 In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a cove.Model 1: Y = β 0 + β 1X1 + β 2X2 + β 3X1X2 + β 4+ β 5X2 + ε where Y = Sale price of property in thousands of dollars X1 = Size of property in thousands of square metres X2 = 1 if property located near cove,0 if not Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown: \(\begin{array}{|l|l|l|l|l|l|} \hline \text { SUMMARY } & \text { OUTPUT } & \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.985 \\ \hline \text { R Square } & & 0.970 \\ \hline \text { Std. Error } & & 9.5 \\ \hline \text { Observations } & & 20 \\ \hline\\ \hline\text { ANOVA }\\ \hline & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \hline \text { Regression } & 5 & 28324 & 5664 & 62.2 & 0.0001 \\ \hline \text { Residual } & 14 & 1279 & 91 & & \\ \hline \text { Total } & 19 & 29603 & & & \\\hline\\ \hline&\text {Coeff }&\text {StdError }&\text {t stat }&\text { P-Value}\\ \hline \text { Intercept } & -32.1 & 35.7 & -0.90 & 0.3834 \\ \hline \text { Size } & 12.2 & 5.9 & 2.05 & 0.0594 \\ \hline \text { Cove } & -104.3 & 53.5 & -1.95 & 0.0715 \\ \hline \text { Size }{ }^{*} \text { Cove } & 17.0 & 8.5 & 1.99 & 0.0661 \\ \hline \text { SizeSq } & -0.3 & 0.2 & -1.28 & 0.2204 \\ \hline \text { SizeSq } & -0.3 & 0.3 & -1.13 & 0.2749 \\\hline \end{array}\) Note: Std.Error = Standard Error -Referring to Instruction 16-3,given a quadratic relationship between sale price (Y)and property size (X1),what test should be used to test whether the curves differ from cove and non-cove properties?

A) F test for the entire regression model. B) Partial F test on the subset of the appropriate coefficients. C) t test on each of the subsets of the appropriate coefficients. D) t test on each of the coefficients in the entire regression model. A) F test for the entire regression model. B) Partial F test on the subset of the appropriate coefficients. C) t test on each of the subsets of the appropriate coefficients. D) t test on each of the coefficients in the entire regression model.

Exam 16: Multiple Regression Model Building

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the model that includes X₁,X₂,X₃,X₅ and X₆should be selected using the adjusted r² statistic.

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Question 81

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,what is the value of the Mallow's C_p statistic for the model that includes X₁,X₅ and X₆?

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Question 82

Two simple regression models were used to predict a single dependent variable.Both models were highly significant,but when the two independent variables were placed in the same multiple regression model for the dependent variable,R² did not increase substantially and the parameter estimates for the model were not significantly different from 0.This is probably an example of collinearity.

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Question 83

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

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Question 84

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the variable X₂ should be dropped to remove collinearity.

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Question 85

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

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Question 86

Using the hat matrix elements h_i to determine influential points in a multiple regression model with k independent variable and n observations,X_i is an influential point if

(Multiple Choice)

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Question 87

Using the best-subsets approach to model building,models are being considered when their

(Multiple Choice)

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Question 88

Instruction 16-7 What are the factors that determine the acceleration time (in sec. )from 0 to 60 kilometres per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu.cm. EP: Engine power KPL: Kilometres per litre SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The coefficient of multiple determination (R²_j)for the regression model using each of the five variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.7461,0.5676,0.6764,0.8582,0.6632 -Referring to Instruction 16-7,what is the value of the variance inflationary factor of Cargo Vol?

(Short Answer)

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Question 89

Evaluating the influence of individual data points using a studentized deleted residual test is usually done with a one-tailed t-test.

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Question 90

Instruction 16-3 In Hawaii,condemnation proceedings are under way to enable private citizens to own the property upon which their homes are built.Until recently,only estates were permitted to own land,and homeowners leased the land from the estate.In order to comply with the new law,a large Hawaiian estate wants to use regression analysis to estimate the fair market value of the land.The following model was fit to data collected for n = 20 properties,10 of which are located near a cove.Model 1: Y = β 0 + β 1X1 + β 2X2 + β 3X1X2 + β 4+ β 5X2 + ε where Y = Sale price of property in thousands of dollars X1 = Size of property in thousands of square metres X2 = 1 if property located near cove,0 if not Using the data collected for the 20 properties,the following partial output obtained from Microsoft Excel is shown: SUMMARY OUTPUT Regression Statistics Multiple R 0.985 R Square 0.970 Std. Error 9.5 Observations 20 ANOVA df SS MS F Signif F Regression 5 28324 5664 62.2 0.0001 Residual 14 1279 91 Total 19 29603 Coeff StdError t stat P-Value Intercept -32.1 35.7 -0.90 0.3834 Size 12.2 5.9 2.05 0.0594 Cove -104.3 53.5 -1.95 0.0715 Size Cove 17.0 8.5 1.99 0.0661 SizeSq -0.3 0.2 -1.28 0.2204 SizeSq -0.3 0.3 -1.13 0.2749 Note: Std.Error = Standard Error -Referring to Instruction 16-3,given a quadratic relationship between sale price (Y)and property size (X1),what test should be used to test whether the curves differ from cove and non-cove properties?

(Multiple Choice)

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Question 91

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the variable X₄ should be dropped to remove collinearity.

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Question 92

Showing 81 - 92 of 92

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

Using the hat matrix elements h_i to determine influential points in a multiple regression model with k independent variable and n observations,X_i is an influential point if

Using the best-subsets approach to model building,models are being considered when their

Evaluating the influence of individual data points using a studentized deleted residual test is usually done with a one-tailed t-test.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

Exam 16: Multiple Regression Model Building

If your data has a non-linear relationship,one transformation that may be useful is the logarithmic transformation.

For a model with 3 independent variables and data set with 75 observations,the denominator degrees of freedom for the Cook's Distance Statistic would be 70.

Using the hat matrix elements hi to determine influential points in a multiple regression model with k independent variable and n observations,Xi is an influential point if

Using the best-subsets approach to model building,models are being considered when their

Evaluating the influence of individual data points using a studentized deleted residual test is usually done with a one-tailed t-test.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

Using the hat matrix elements h_i to determine influential points in a multiple regression model with k independent variable and n observations,X_i is an influential point if