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}{ll}\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 $\begin{array}{llllll} & d f & \text { SS } & \text { MS } & F & \text { Siguif } F \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array}{lllll} & \text { Coeff } & \text { StdError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \\ \text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-4,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. A

Instruction 13-8 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premium depends very much on the age of the individual,the number of traffic tickets received by the individual,and the population density of the city in which the individual lives.You performed a regression analysis in Microsoft Excel and obtained the following information: $\begin{array}{l} \text { Regression Analysis }\\ \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.63 \\ \text { R Square } & 0.40 \\ \text { Adjusted R Square } & 0.23 \\ \text { Standard Error } & 50.00 \\ \text { Observations } & 15.00 \\ \hline \end{array} \end{array}$ ANOVA $\begin{array}{lrrrrrr} \hline & d f & & S S & M S & F & \text { Significance } F \\ \hline \text { Regression } & 3 & & 5994.24 & 2.40 & 0.12 \\ \text { Residual } & 11 & 27496.82 & & & \\ \text { Total } & & & 45479.54 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & P \text {-value } & \text { Lower 99.0\% } & \text { Upper 99.0\% } \\ \hline \text { Intercept } & 123.80 & 48.71 & 2.54 & 0.03 & -27.47 & 275.07 \\ \text { AGE } & -0.82 & 0.87 & -0.95 & 0.36 & -3.51 & 1.87 \\ \text { TICKETS } & 21.25 & 10.66 & 1.99 & 0.07 & -11.86 & 54.37 \\ \text { DENSITY } & -3.14 & 6.46 & -0.49 & 0.64 & -23.19 & 16.91 \\ \hline \end{array}$ -Referring to Instruction 13-8,the proportion of the total variability in insurance premiums that can be explained by AGE,TICKETS,and DENSITY is ________.

The answer of Instruction 13-8 You worked as an intern at...

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) XS1U1B11 S1U1B0= Length of time in weight-loss program (in months) XS1U1B12S1U1B0 = 1 if morning session,0 if not XS1U1B13S1U1B0 = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + βS1U1B11S1U1B0XS1U1B11S1U1B0 + βS1U1B12S1U1B0XS1U1B12S1U1B0 + βS1U1B13S1U1B0XS1U1B13S1U1B0 + βS1U1B14S1U1B0XS1U1B11S1U1B0XS1U1B12S1U1B0 + βS1U1B15S1U1B0XS1U1B11S1U1B0XS1U1B13S1U1B0 + ε Partial output from Microsoft Excel follows: Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.73514 \\ \text { R Square } & 0.540438 \\ \text { Adjusted R Square } & 0.157469 \\ \text { Standard Error } & 12.4147 \\ \text { Observations } & 12 \end{array}$ ANOVA $\begin{array} { c c c c c } F = 5.41118 & \text { Significance } F = 0.040201 & & \\ & & & & \\ \text { Intercept } & \text { Coeff } & \text { StdError } & t \text { Stat } & P \text {-value } \\ \text { Length } \left( X _ { 1 } \right) & 0.089744 & 14.127 & 0.0060 & 0.9951 \\ \text { Morn Ses } \left( X _ { 2 } \right) & 6.22538 & 2.43473 & 2.54956 & 0.0479 \\ \text { Aft Ses } \left( X _ { 3 } \right) & 2.217272 & 22.1416 & 0.100141 & 0.9235 \\ \text { Length*Morn Ses } & 11.8233 & 3.1545 & 3.558901 & 0.0165 \\ \text { Length*Aft Ses } & 0.77058 & 3.562 & 0.216334 & 0.8359 \\ & - 0.54147 & 3.35988 & - 0.161158 & 0.8773 \end{array}$ -Referring to Instruction 13-9,which of the following statements is supported by the analysis shown?

A) There is sufficient evidence (at ? = 0.05)of curvature in the relationship between weight-loss (Y)and months in program(X1). B) There is sufficient evidence (at ? = 0.10)to indicate that the session time (morning,afternoon,evening)affects weight-loss (Y). C) There is sufficient evidence (at ? = 0.05)to indicate that the relationship between weight-loss (Y)and months in program (X1)depends on session time. D) There is insufficient evidence (at ? = 0.10)to indicate that the relationship between weight-loss (Y)and months in program(X1)depends on session time. A) There is sufficient evidence (at ? = 0.05)of curvature in the relationship between weight-loss (Y)and months in program(X1). B) There is sufficient evidence (at ? = 0.10)to indicate that the session time (morning,afternoon,evening)affects weight-loss (Y). C) There is sufficient evidence (at ? = 0.05)to indicate that the relationship between weight-loss (Y)and months in program (X1)depends on session time. D) There is insufficient evidence (at ? = 0.10)to indicate that the relationship between weight-loss (Y)and months in program(X1)depends on session time.

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. SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adj. R Square } & 0.976 \\ \text { Std. Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signiff } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StaError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-3,when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable,he obtained an r2 value of 0.971.What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?

A) 98.2 B) 1.1 C) 11.1 D) 2.8 A) 98.2 B) 1.1 C) 11.1 D) 2.8

Instruction 13-10 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. $\begin{array}{l} \text { Regression Statistics }\\ \begin{array}{lr} \hline \text { Multiple R } & 0.9659 \\ \text { R Square } & 0.9331 \\ \text { Adjusted R Square } & 0.9294 \\ \text { Standard Error } & 0.0327 \\ \text { Observations } & 58 \end{array} \end{array}$ ANOVA $\begin{array}{lrrrrr} & D f & S S & M S & F & \text { Significance F } \\ \hline \text { Regression } & 3 & 0.8094 & 0.2698 & 251.1995 & 0.0000 \\ \text { Residual } & 54 & 0.0580 & 0.0010 & & \\ \text { Total } & 57 & 0.8675 & & & \end{array}$ $\begin{array}{lrrrr} & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {P \text {-value }} \\ \hline \text { Intercept } & 0.5118 & 0.0136 & 37.4675 & 2.4904 \\ \mathrm{X}_{1} & -0.0045 & 0.0034 & -1.3276 & 0.1898 \\ \mathrm{X}_{2} & -0.2392 & 0.0123 & -19.3942 & 0.0000 \\ \mathrm{X}_{3} & -0.0002 & 0.0123 & -0.0214 & 0.9829 \end{array}$ -Referring to Instruction 13-10,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.

Instruction 13-1 A manager of a product sales group believes the number of sales made by an employee (Y)depends on how many years that employee has been with the company (XS1U1B11S1U1B0)and how he/she scored on a business aptitude test (XS1U1B12S1U1B0).A random sample of 8 employees provides the following: \[\begin{array} { | l | l | l | l | } \hline \text { Employee } & \text { Y } & \text { XI } & \text { X2 } \\ \hline 1 & 100 & 10 & 7 \\ \hline 2 & 90 & 3 & 10 \\ \hline 3 & 80 & 8 & 9 \\ \hline 4 & 70 & 5 & 4 \\ \hline 5 & 60 & 5 & 8 \\ \hline 6 & 50 & 7 & 5 \\ \hline 7 & 40 & 1 & 4 \\ \hline 8 & 30 & 1 & 1 \\ \hline \end{array}\] -Referring to Instruction 13-1,for these data,what is the value for the regression constant,b0?

A) 0.998 B) 21.293 C) 3.103 D) 4.698 A) 0.998 B) 21.293 C) 3.103 D) 4.698

Instruction 13-16 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. \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adjusted R } & 0.4030 \\ \text { Square } & \\ \text { Standard } & 18.4861 \\ \text { Error } \\ \text { Observations } & 40 \\ \hline \end{array}\] ANOVA $\begin{array}{lrrrrrr} & \text { df } & \text { SS } & {\text { MS }} & \text { F } & \text { Significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067& 7.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 &2.0238\\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402\\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 &1.2618\\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \end{array}$ 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: \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40\\ \hline \end{array}\] \[\begin{array}{l} \text { ANOVA }\\ \begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to Instruction 13-16 Model 1,what is the p-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 13-16 Given below are results from the...

Instruction 13-13 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, XS1U1B11S1U1B0 = % Attendance,XS1U1B12 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \text { R Square } & 0.6288 \\ \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \text { Observations } & 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & d f & {\text { SS }} & M S & F & \text { Significance } F \\ \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\ \text { Residual } & 43 & 4702.02 & 109.35 & & \\ \text { Total } & 46 & 12667.11 & & & \end{array}$ $\begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\ \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \end{array}$ -Referring to Instruction 13-13,which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

A) H1: ?0 ? 0 B) H1: ?1 ? 0 C) H1: ?3 ? 0 D) H1: ?2 ? 0 A) H1: ?0 ? 0 B) H1: ?1 ? 0 C) H1: ?3 ? 0 D) H1: ?2 ? 0

Instruction 13-15 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 variables: age (XS1U1B11S1U1B0 = Age),experience in the field (XS1U1B12S1U1B0 = Exper),number of degrees (XS1U1B13S1U1B0 = Degrees),and number of previous jobs in the field (XS1U1B14S1U1B0 = Prevjobs).He took a sample of 20 employees and obtained the following Microsoft Excel output: SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.992 \\ \text { R Square } & 0.984 \\ \text { Adj. R Square } & 0.979 \\ \text { Std. Error } & 2.26743 \\ \text { Observations } & 20 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signif } \boldsymbol { F } \\ \text { Regression } & 4 & 4609.83164 & 1152.45791 & 224.160 & 0.0001 \\ \text { Residual } & 15 & 77.11836 & 5.14122 & & \\ \text { Total } & 19 & 4686.95000 & & & \end{array}$ $\begin{array} { l l l l l } & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } \\ \text { Intercept } & - 9.611198 & 2.77988638 & - 3.457 & 0.0035 \\ \text { Age } & 1.327695 & 0.11491930 & 11.553 & 0.0001 \\ \text { Exper } & - 0.106705 & 0.14265559 & - 0.748 & 0.4660 \\ \text { Degrees } & 7.311332 & 0.80324187 & 9.102 & 0.0001 \\ \text { Prevjobs } & - 0.504168 & 0.44771573 & - 1.126 & 0.2778 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-15,the p-value of the F test for the significance of the entire regression is ________.

The answer of Instruction 13-15 A financial analyst wanted to examine...

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. $\quad\quad\quad\quad\quad$OUTPUT SUMMARY Regression $\quad$Statistics $\begin{array} { l l } \text { Multiple R } && 0.991 \\ \text { R Square } && 0.982 \\ \text { Adj. R Square } && 0.976 \\ \text { Std. Error } && 0.299 \\ \text { Observations } && 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { SignifF } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StaError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ 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 13-16 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. \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adjusted R } & 0.4030 \\ \text { Square } & \\ \text { Standard } & 18.4861 \\ \text { Error } \\ \text { Observations } & 40 \\ \hline \end{array}\] ANOVA $\begin{array}{lrrrrrr} & \text { df } & \text { SS } & {\text { MS }} & \text { F } & \text { Significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067& 7.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 &2.0238\\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402\\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 &1.2618\\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \end{array}$ 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: \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40\\ \hline \end{array}\] \[\begin{array}{l} \text { ANOVA }\\ \begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to Instruction 13-16 Model 1,what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one year increase in education received on the mean number of weeks a worker is unemployed due to a layoff after taking into consideration the effect of all the other independent variables?

The answer of Instruction 13-16 Given below are results from the...

Instruction 13-16 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. \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.7035 \\ \text { R Square } & 0.4949 \\ \text { Adjusted R } & 0.4030 \\ \text { Square } & \\ \text { Standard } & 18.4861 \\ \text { Error } \\ \text { Observations } & 40 \\ \hline \end{array}\] ANOVA $\begin{array}{lrrrrrr} & \text { df } & \text { SS } & {\text { MS }} & \text { F } & \text { Significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067& 7.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 &2.0238\\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402\\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 &1.2618\\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \end{array}$ 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: \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40\\ \hline \end{array}\] \[\begin{array}{l} \text { ANOVA }\\ \begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to Instruction 13-16 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 13-16 Given below are results from the...

Exam 13: Introduction to Multiple Regression

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 Siguif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff StdError Stat -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,which of the independent variables in the model are significant at the 5% level?

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Question 1

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A

Instruction 13-16 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. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error Observations 40 ANOVA df SS MS F Significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% 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: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 ANOVA df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error 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 13-16 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.

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Question 2

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A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

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Question 3

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A dummy variable is used as an independent variable in a regression model when

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Question 4

Instruction 13-8 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premium depends very much on the age of the individual,the number of traffic tickets received by the individual,and the population density of the city in which the individual lives.You performed a regression analysis in Microsoft Excel and obtained the following information: Regression Analysis Regression Statistics Multiple R 0.63 R Square 0.40 Adjusted R Square 0.23 Standard Error 50.00 Observations 15.00 ANOVA df SS MS F Significance F Regression 3 5994.24 2.40 0.12 Residual 11 27496.82 Total 45479.54 Coefficients Standard Error t Stat P -value Lower 99.0\% Upper 99.0\% Intercept 123.80 48.71 2.54 0.03 -27.47 275.07 AGE -0.82 0.87 -0.95 0.36 -3.51 1.87 TICKETS 21.25 10.66 1.99 0.07 -11.86 54.37 DENSITY -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Instruction 13-8,the proportion of the total variability in insurance premiums that can be explained by AGE,TICKETS,and DENSITY is ________.

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Question 5

A regression had the following results: SST = 102.55,SSE = 82.04.It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

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Question 6

Instruction 13-9 A weight-loss clinic wants to use regression analysis to build a model for weight-loss of a client (measured in kilograms).Two variables thought to effect weight-loss are client's length of time on the weight loss program and time of session.These variables are described below: Y = Weight-loss (in kilograms) X₁= Length of time in weight-loss program (in months) X₂ = 1 if morning session,0 if not X₃ = 1 if afternoon session,0 if not (Base level = evening session) Data for 12 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β0 + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₁X₂ + β₅X₁X₃ + ε Partial output from Microsoft Excel follows: Regression Statistics Multiple R 0.73514 R Square 0.540438 Adjusted R Square 0.157469 Standard Error 12.4147 Observations 12 ANOVA F=5.41118 Significance F=0.040201 Intercept Coeff StdError t Stat P -value Length 0.089744 14.127 0.0060 0.9951 Morn Ses 6.22538 2.43473 2.54956 0.0479 Aft Ses 2.217272 22.1416 0.100141 0.9235 LengthMorn Ses 11.8233 3.1545 3.558901 0.0165 LengthAft Ses 0.77058 3.562 0.216334 0.8359 -0.54147 3.35988 -0.161158 0.8773 -Referring to Instruction 13-9,which of the following statements is supported by the analysis shown?

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Question 7

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. SUMMARY Regression Statistics Multiple R 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA SS MS Signiff Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StaError Stat -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,when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable,he obtained an r² value of 0.971.What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?

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Question 8

Instruction 13-10 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. Regression Statistics Multiple R 0.9659 R Square 0.9331 Adjusted R Square 0.9294 Standard Error 0.0327 Observations 58 ANOVA Df SS MS F Significance F Regression 3 0.8094 0.2698 251.1995 0.0000 Residual 54 0.0580 0.0010 Total 57 0.8675 Coefficients Standard Error t Stat P -value Intercept 0.5118 0.0136 37.4675 2.4904 -0.0045 0.0034 -1.3276 0.1898 -0.2392 0.0123 -19.3942 0.0000 -0.0002 0.0123 -0.0214 0.9829 -Referring to Instruction 13-10,what is the correct interpretation for the estimated coefficient for x₂?

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Question 9

Instruction 13-1 A manager of a product sales group believes the number of sales made by an employee (Y)depends on how many years that employee has been with the company (X₁)and how he/she scored on a business aptitude test (X₂).A random sample of 8 employees provides the following: Employee Y XI X2 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 -Referring to Instruction 13-1,for these data,what is the value for the regression constant,b₀?

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Question 10

Instruction 13-16 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. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error Observations 40 ANOVA df SS MS F Significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P -value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 7.8257 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: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 ANOVA df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error 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 13-16 Model 1,what is the p-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 11

Instruction 13-13 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: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA df SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Instruction 13-13,which of the following is the correct alternative hypothesis to test whether instructional spending per pupil has any effect on percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

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Question 12

Instruction 13-15 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 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: SUMMARY Regression Statistics Multiple R 0.992 R Square 0.984 Adj. R Square 0.979 Std. Error 2.26743 Observations 20 ANOVA SS MS Signif Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coeff StdError Stat -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 13-15,the p-value of the F test for the significance of the entire regression is ________.

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Question 13

Instruction 13-14 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: SUMMARY Regression Statistics Multiple R 0.916 R Square 0.839 Adj. R Square 0.732 Std. Error 0.24685 Observations 6 ANOVA SS MS Signif Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError Stat -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 13-14,the net regression coefficient of X₂ is ________.

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Question 14

Instruction 13-14 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: SUMMARY Regression Statistics Multiple R 0.916 R Square 0.839 Adj. R Square 0.732 Std. Error 0.24685 Observations 6 ANOVA SS MS Signif Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError Stat -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 13-14,the Head of Department wants to use a t test to test for the significance of the coefficient of X₁.For a level of significance of 0.05,the critical values of the test are ________.

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Question 15

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. $\quad\quad\quad\quad\quad$ OUTPUT SUMMARY Regression $\quad$ Statistics Multiple R 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA SS MS SignifF Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StaError Stat -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?

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Question 16

Instruction 13-15 A financial analyst wanted to examine the relationship between salary (in $1,000)and 4 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: SUMMARY Regression Statistics Multiple R 0.992 R Square 0.984 Adj. R Square 0.979 Std. Error 2.26743 Observations 20 ANOVA SS MS Signif Regression 4 4609.83164 1152.45791 224.160 0.0001 Residual 15 77.11836 5.14122 Total 19 4686.95000 Coeff StdError Stat -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 13-15,the analyst wants to use a t test to test for the significance of the coefficient of X₃.The p-value of the test is ________.

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Question 17

Instruction 13-16 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. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error Observations 40 ANOVA df SS MS F Significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P -value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 7.8257 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: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 ANOVA df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error 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 13-16 Model 1,what are the lower and upper limits of the 95% confidence interval estimate for the effect of a one year increase in education received on the mean number of weeks a worker is unemployed due to a layoff after taking into consideration the effect of all the other independent variables?

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Question 18

Instruction 13-16 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. Regression Statistics Multiple R 0.7035 R Square 0.4949 Adjusted R 0.4030 Square Standard 18.4861 Error Observations 40 ANOVA df SS MS F Significance F Regression 6 11048.6415 1841.4402 5.3885 0.00057 Residual 33 11277.2586 341.7351 Total 39 22325.9 Coefficients Standard Error t Stat P -value Lower 95\% Upper 95\% Intercept 32.6595 23.18302 1.4088 0.1683 -14.5067 7.8257 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: Regression Statistics Multiple R 0.6391 R Square 0.4085 Adjusted R 0.3765 Square Standard Error 18.8929 Observations 40 ANOVA df SS MS F Significance F Regression 2 9119.0897 4559.5448 12.7740 0.0000 Residual 37 13206.8103 356.9408 Total 39 22325.9 Coefficients Standard Error 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 13-16 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 19

Instruction 13-13 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: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA df SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Instruction 13-13,what is the value of 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?

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Question 20

A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

A dummy variable is used as an independent variable in a regression model when

A regression had the following results: SST = 102.55,SSE = 82.04.It can be said that 20.0% of the variation in the dependent variable is explained by the independent variables in the regression.

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

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

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