Instruction 13.37 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adj. R Square } & 0.4030 \\ \text { Std. Error } & 18.4861 \\ \text { Observations } & 40 \end{array}$ ANOVA $\begin{array} { l l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } & \\ \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 & \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & & \\ \text { Total } & 39 & 223325.9 & & & & \\ & & & & & & \\ & \text { Coeff } & \text { StdError } & \text { tStat } & p \text { value } & \text { Lower 95\% } & \text { Upper95\% } \\ \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\ \text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\ \text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\ \text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \end{array}$ Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adj. R Square } & 0.3765 \\ \text { Std. Error } & 18.8929 \\ \text { Observations } & 40 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 & \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 & \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 & \end{array}$ -Referring to Instruction 13.37 Model 1,which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

A) H0: ?3 = 0 B) H0: ?4 = 0 C) H0: ?2 = 0 D) H0: ?1 = 0 A) H0: ?3 = 0 B) H0: ?4 = 0 C) H0: ?2 = 0 D) H0: ?1 = 0

Instruction 13.37 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adj. R Square } & 0.4030 \\ \text { Std. Error } & 18.4861 \\ \text { Observations } & 40 \end{array}$ ANOVA $\begin{array} { l l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } & \\ \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 & \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & & \\ \text { Total } & 39 & 223325.9 & & & & \\ & & & & & & \\ & \text { Coeff } & \text { StdError } & \text { tStat } & p \text { value } & \text { Lower 95\% } & \text { Upper95\% } \\ \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & - 14.5067 & 79.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \text { Edu } & - 1.3537 & 1.1766 & - 1.1504 & 0.2582 & - 3.7476 & 1.0402 \\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & - 0.5914 & 1.8257 \\ \text { Married } & - 5.2189 & 7.6068 & - 0.6861 & 0.4974 & - 20.6950 & 10.2571 \\ \text { Head } & - 14.2978 & 7.6479 & - 1.8695 & 0.0704 & - 29.8575 & 1.2618 \\ \text { Manager } & - 24.8203 & 11.6932 & - 2.1226 & 0.0414 & - 48.6102 & - 1.0303 \end{array}$ Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adj. R Square } & 0.3765 \\ \text { Std. Error } & 18.8929 \\ \text { Observations } & 40 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 & \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 & \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 & \end{array}$ -Referring to Instruction 13.37 Model 1,what is the value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

The answer of Instruction 13.37 Given below are results from the...

Instruction 13.4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adj. R Square } & 0.726 \\ \text { Std. Error } & 5.195 \\ \text { Observations } & 50 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F} \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 & \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 & \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 & \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.4,what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square metre home (House = 100)?

A) $178.33 thousand. B) $211.85 thousand. C) $44.14 thousand. D) $56.75 thousand. A) $178.33 thousand. B) $211.85 thousand. C) $44.14 thousand. D) $56.75 thousand.

Instruction 13.29 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics $\begin{array} { l l } \text { MultipleR } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adj. R Square } & 0.976 \\ \text { Std. Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.29,to test for the significance of the coefficient on gross domestic product,the p-value is

A) 0.0001. B) 0.9999. C) 0.8330. D) 0.8837. A) 0.0001. B) 0.9999. C) 0.8330. D) 0.8837.

Instruction 13.3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics $\begin{array} { l l } \text { MultipleR } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adj. R Square } & 0.976 \\ \text { Std. Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.3,what is the estimated average consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

A) $1.39 billion. B) $2.89 billion. C) $4.75 billion. D) $9.45 billion. A) $1.39 billion. B) $2.89 billion. C) $4.75 billion. D) $9.45 billion.

Instruction 13.40 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Sydney and Melbourne. He believes that the appropriate model is \[Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }\] where $\begin{array} { l } x _ { 1 } = \text { mortgage rate in } \% \\ x _ { 2 } = 1 \text { if Sydney, } 0 \text { if Melbourne } \\ Y = \text { demand in } \$ 100 \text { per capita } \end{array}$ -Referring to Instruction 13.40,the fitted model for predicting demand in Melbourne is ______.

A) S1U1B0S1U1B1 S1U1B015 + 8XS1U1B12S1U1B0 B) S1U1B0S1U1B1 S1U1B010 + 13XS1U1B11S1U1B0 C) S1U1B0S1U1B1 S1U1B018 + 5XS1U1B12S1U1B0 D) S1U1B0S1U1B1 S1U1B010 + 5XS1U1B11S1U1B0 A) S1U1B0S1U1B1 S1U1B015 + 8XS1U1B12S1U1B0 B) S1U1B0S1U1B1 S1U1B010 + 13XS1U1B11S1U1B0 C) S1U1B0S1U1B1 S1U1B018 + 5XS1U1B12S1U1B0 D) S1U1B0S1U1B1 S1U1B010 + 5XS1U1B11S1U1B0

Instruction 13.30 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adj. R Square } & 0.726 \\ \text { Std. Error } & 5.195 \\ \text { Observations } & 50 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signiff } \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 5.8078 & - 0.281 & 0.7798 & \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 & \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 & \\ \text { School } & - 0.6517 & 0.4319 & - 1.509 & 0.1383 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.30,which of the independent variables in the model are significant at the 5% level?

A) Income, Size. B) Income, School. C) Size, School. D) Income, Size, School. A) Income, Size. B) Income, School. C) Size, School. D) Income, Size, School.

Instruction 13.3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics $\begin{array} { l l } \text { MultipleR } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adj. R Square } & 0.976 \\ \text { Std. Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Signif F } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StdError } & t \text { Stat } & p \text { value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.3,what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

A) $1.39 billion. B) $2.89 billion. C) $4.75 billion. D) $9.45 billion. A) $1.39 billion. B) $2.89 billion. C) $4.75 billion. D) $9.45 billion.

Instruction 13.39 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, number of city blocks to the centre of the university, and one of the three jurisdictions: on campus, in the CBD and off campus, or outside of the CBD and off campus. The population regression model hypothesised is: Yi = α + βS1U1B11S1U1B0xS1U1B11S1U1B0S1U1B1iS1U1B0 + βS1U1B12S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + βS1U1B13S1U1B0xS1U1B12S1U1B0S1U1B1iS1U1B0 + εS1U1B1iS1U1B0 Where Y is the meter price xS1U1B11S1U1B0 is the number of blocks to the centre of the university xS1U1B12S1U1B0 is a dummy variable that takes the value 1 if the meter is located in the CBD and off campus and the value 0 otherwise xS1U1B13S1U1B0 is a dummy variable that takes the value 1 if the meter is located outside of the CBD and off campus, and the value 0 otherwise The following Excel results are obtained. -Referring to Instruction 13.39,what is the correct interpretation for the estimated coefficient for x2?

A) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking on campus, and parking outside of the CBD and off campus is $0.24 per hour. B) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking on campus is $0.24 per hour. C) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking either outside of the CBD and off campus or on campus is $0.24 per hour. D) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking outside of the CBD and off campus is $0.24 per hour. A) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking on campus, and parking outside of the CBD and off campus is $0.24 per hour. B) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking on campus is $0.24 per hour. C) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking either outside of the CBD and off campus or on campus is $0.24 per hour. D) Holding the effect of the other independent variables constant, the estimated mean difference in costs between parking in the CBD and off campus, and parking outside of the CBD and off campus is $0.24 per hour.

Exam 13: Introduction to Multiple Regression

Instruction 13.37 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40 ANOVA df SS MS F Signif F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 223325.9 Coeff StdError tStat p value Lower 95\% Upper95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40 ANOVA df SS MS F Signif F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coeff StdError t Stat p value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Instruction 13.37 Model 1,which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

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Question 81

Instruction 13.37 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40 ANOVA df SS MS F Signif F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 223325.9 Coeff StdError tStat p value Lower 95\% Upper95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40 ANOVA df SS MS F Signif F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coeff StdError t Stat p value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Instruction 13.37 Model 1,what is the value of the test statistic when testing whether being married or not makes a difference in the mean number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

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Question 82

Instruction 13.13 A financial analyst wanted to examine the relationship between salary (in $1,000) and four variables: age (X₁ = Age), experience in the field (X₂ = Exper), number of degrees (X₃ = Degrees) and number of previous jobs in the field (X₄ = Prevjobs). He took a sample of 20 employees and obtained the following Microsoft Excel output: $\text { OUTPUT }$ SUMMARY Regression Statistics Multiple R 0.992 R Square 0.984 Adj. R Square 0.979 Std. Error 2.26743 Observations 20 ANOVA df SS MS F Signif F Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coeff Std Error t Stat p value Intercept -9.611198 2.77988638 -3.457 0.0035 Age 1.327695 0.11491930 11.553 0.0001 Exper -0.106705 0.14265559 -0.748 0.4660 Degrees 7.311332 0.80324187 9.102 0.0001 Prevjobs -0.504168 0.44771573 -1.126 0.2778 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.13,the analyst wants to use an F test to test H₀: $\beta$ ₁ = $\beta$ ₂ = $\beta$ ₃= $\beta$ ₄= 0.The appropriate alternative hypothesis is ___________

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Question 83

Instruction 13.22 The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries) and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: -Referring to Instruction 13.22,what is the standard error of estimate?

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Question 84

AU: Question 37 is the same as Question 36. Please check. Instruction 13.12 AU: Please advise if Instruction 13.12 can be renumbered to Instruction 13.11 and further questions renumbered. Or advise whether there shall be new Instruction 13.11 included. The Head of the Accounting Department wanted to see if she could predict the average grade of students using the number of course units (credits) and total university entrance exam scores of each. She takes a sample of students and generates the following Microsoft Excel output: OUTPUT SUMMARY Regression Statistics MultipleR 0.916 R Square 0.839 Adj. R Square 0.732 Std. Error 0.24685 Observations 6 ANOVA df SS MS F Signiff Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError t Stat p value Intercept 4.593897 1.13374542 4.052 0.0271 GDP -0.247270 0.06268485 -3.945 0.0290 Price 0.001443 0.00101241 1.425 0.2494 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.12,the value of the adjusted coefficient of multiple determination,r²adj,is ___________.

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Question 85

Instruction 13.4 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics Multiple R 0.865 R Square 0.748 Adj. R Square 0.726 Std. Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff StdError t Stat p value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.4,what minimum annual income would an individual with a family size of 4 and 16 years of education need to attain a predicted 10,000 square metre home (House = 100)?

(Multiple Choice)

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Question 86

Instruction 13.33 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Sydney and Melbourne. He believes that the appropriate model is Y=10+5+8 where = mortgage rate in \% =1 if Sydney, 0 if Melbourne Y = demand in \ 100 per capita -Referring to Instruction 13.33,the predicted demand in Sydney when the mortgage rate is 10% is ___________ per capita.

(Short Answer)

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Question 87

Instruction 13.37 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40 ANOVA df SS MS F Signif F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 223325.9 Coeff StdError tStat p value Lower 95\% Upper95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40 ANOVA df SS MS F Signif F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coeff StdError t Stat p value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Instruction 13.37 Model 1,the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff.

(True/False)

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Question 88

Instruction 13.29 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics MultipleR 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA df SS MS F Signiff Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat p value Intercept -1.6335 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.29,to test for the significance of the coefficient on gross domestic product,the p-value is

(Multiple Choice)

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Question 89

Instruction 13.22 The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries) and instructional spending per pupil in dollars (Spending) of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance, X₂= Salaries and X₃= Spending: -Referring to Instruction 13.22,what are the numerator and denominator degrees of freedom,respectively,for the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables?

(Short Answer)

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Question 90

Instruction 13.3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics MultipleR 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat p value Intercept -1.6335 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.3,what is the estimated average consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

(Multiple Choice)

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Question 91

Instruction 13.40 An econometrician is interested in evaluating the relation of demand for building materials to mortgage rates in Sydney and Melbourne. He believes that the appropriate model is $Y = 10 + 5 X _ { 1 } + 8 X _ { 2 }$ where = mortgage rate in \% =1 if Sydney, 0 if Melbourne Y= demand in \ 100 per capita -Referring to Instruction 13.40,the fitted model for predicting demand in Melbourne is ______.

(Multiple Choice)

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Question 92

Instruction 13.25 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40 ANOVA df SS MS F Signiff Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 223325.9 Coeff StdError tStat p value Lower 95\% Upper95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40 ANOVA df SS MS F Signiff Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coeff StdError t Stat p value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Instruction 13.25 Model 1,there is sufficient evidence that the number of weeks a worker is unemployed due to a layoff depends on all of the explanatory variables at a 10% level of significance.

(True/False)

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Question 93

When an additional explanatory variable is introduced into a multiple regression model,the coefficient of multiple determination will never decrease.

(True/False)

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Question 94

Instruction 13.30 A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size) and education of the head of household (School). House size is measured in hundreds of square metres, income is measured in thousands of dollars and education is in years. The builder randomly selected 50 families and ran the multiple regression. Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics Multiple R 0.865 R Square 0.748 Adj. R Square 0.726 Std. Error 5.195 Observations 50 ANOVA df SS MS F Signiff Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff StdError t Stat p value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.30,which of the independent variables in the model are significant at the 5% level?

(Multiple Choice)

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Question 95

Instruction 13.2 A lecturer in industrial relations believes that an individual's wage rate at a factory (Y) depends on his performance rating (X₁) and the number of economics courses the employee successfully completed at university (X₂). The lecturer randomly selects six workers and collects the following information: Employee Y(\ ) X1 X2 1 10 3 0 2 12 1 5 3 15 8 1 4 17 5 8 5 20 7 12 6 25 10 9 -Referring to Instruction 13.2,for these data,what is the estimated coefficient for the number of economics courses taken,b₂?

(Multiple Choice)

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Question 96

Instruction 13.3 An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below. OUTPUT SUMMARY Regression Statistics MultipleR 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA df SS MS F Signif F Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StdError t Stat p value Intercept -1.6335 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 Note: Adj. R Square = Adjusted R Square; Std. Error = Standard Error -Referring to Instruction 13.3,what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

(Multiple Choice)

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Question 97

Instruction 13.25 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy) and the independent variables are the age of the worker (Age), the number of years of education received (Edu), the number of years at the previous job (Job Yr), a dummy variable for marital status (Married: 1 = married, 0 = otherwise), a dummy variable for head of household (Head: 1 = yes, 0 = no) and a dummy variable for management position (Manager: 1 = yes, 0 = no). We shall call this Model 1. Model 1 Regression Statistics Multiple R 0.7035 R Square 0.4949 Adj. R Square 0.4030 Std. Error 18.4861 Observations 40 ANOVA df SS MS F Signiff Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 223325.9 Coeff StdError tStat p value Lower 95\% Upper95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 79.8257 Age 1.2915 0.3599 3.5883 0.0011 0.5592 2.0238 Edu -1.3537 1.1766 -1.1504 0.2582 -3.7476 1.0402 Job Yr 0.6171 0.5940 1.0389 0.3064 -0.5914 1.8257 Married -5.2189 7.6068 -0.6861 0.4974 -20.6950 10.2571 Head -14.2978 7.6479 -1.8695 0.0704 -29.8575 1.2618 Manager -24.8203 11.6932 -2.1226 0.0414 -48.6102 -1.0303 Model 2 is the regression analysis where the dependent variable is Unemploy and the independent variables are Age and Manager. The results of the regression analysis are given below: Mode 2 Regression Statistics Multiple R 0.6391 R Square 0.4085 Adj. R Square 0.3765 Std. Error 18.8929 Observations 40 ANOVA df SS MS F Signiff Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coeff StdError t Stat p value Intercept -0.2143 11.5796 -0.0185 0.9853 Age 1.4448 0.3160 4.5717 0.0000 Manager -22.5761 11.3488 -1.9893 0.0541 -Referring to Instruction 13.25 Model 1,you can conclude that,holding constant the effect of the other independent variables,the number of years of education received has no impact on the mean number of weeks a worker is unemployed due to a layoff at a 5% level of significance if you use only the information of the 95% confidence interval estimate for ?₂.

(True/False)

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Question 98

Instruction 13.39 As a project for his business statistics class, a student examined the factors that determined parking meter rates throughout the campus area. Data were collected for the price per hour of parking, number of city blocks to the centre of the university, and one of the three jurisdictions: on campus, in the CBD and off campus, or outside of the CBD and off campus. The population regression model hypothesised is: Yi = α + β₁x₁_i + β₂x₂_i + β₃x₂_i + ε_i Where Y is the meter price x₁ is the number of blocks to the centre of the university x₂ is a dummy variable that takes the value 1 if the meter is located in the CBD and off campus and the value 0 otherwise x₃ is a dummy variable that takes the value 1 if the meter is located outside of the CBD and off campus, and the value 0 otherwise The following Excel results are obtained. -Referring to Instruction 13.39,what is the correct interpretation for the estimated coefficient for x₂?

(Multiple Choice)

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Question 99

A regression equation is computed on a sample of 40 cases and includes two predictor variables.The degrees of freedom for the partial F statistic are ___________.

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Question 100

When an additional explanatory variable is introduced into a multiple regression model,the coefficient of multiple determination will never decrease.

A regression equation is computed on a sample of 40 cases and includes two predictor variables.The degrees of freedom for the partial F statistic are ___________.

Defining and Collecting Data

Organising and Visualising Data

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

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality Management

Further Non-Parametric Tests

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