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 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?

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 $\begin{array}{lrrrrr} & \text { df } &{\text { SS }} & \text { MS } & F&\text { Significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067 & 79.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402 \\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 & 1.2618 \\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \end{array}$ 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: \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40\\ \hline \end{array}\] \[\begin{array}{l} \text { ANOVA }\\ \begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to Instruction 13-16 Model 1,which of the following is the correct null hypothesis to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

A) H0: ?0 = ?1 = ?2 = ?3 = ?4 = ?5 = ?6 = 0 B) H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 C) H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 = 0 D) H0: ?0 = ?1 = ?2 = ?3 = ?4 = ?5 = ?6 A) H0: ?0 = ?1 = ?2 = ?3 = ?4 = ?5 = ?6 = 0 B) H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 C) H0: ?1 = ?2 = ?3 = ?4 = ?5 = ?6 = 0 D) H0: ?0 = ?1 = ?2 = ?3 = ?4 = ?5 = ?6

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

A) 50 B) 3 C) 49 D) 46 A) 50 B) 3 C) 49 D) 46

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 $\begin{array}{lrrrrr} & \text { df } &{\text { SS }} & \text { MS } & F&\text { Significance F } \\ \hline \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067 & 79.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402 \\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 & 1.2618 \\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \end{array}$ 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: \[\begin{array} { l r } \hline { \text { Regression Statistics } } \\ \hline \text { Multiple R } & 0.6391 \\ \text { R Square } & 0.4085 \\ \text { Adjusted R } & 0.3765 \\ \text { Square } & \\ \text { Standard Error } & 18.8929 \\ \text { Observations } & 40\\ \hline \end{array}\] \[\begin{array}{l} \text { ANOVA }\\ \begin{array} { l r r r l r } \hline & d f & { S S } & { M S } & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 9119.0897 & 4559.5448 & 12.7740 & 0.0000 \\ \text { Residual } & 37 & 13206.8103 & 356.9408 & & \\ \text { Total } & 39 & 22325.9 & & & \\ \hline \end{array}\\ \begin{array} { l r r r r } \hline & \text { Coefficients } & \text { Standard Error } & { t \text { Stat } } & P \text {-value } \\ \hline \text { Intercept } & - 0.2143 & 11.5796 & - 0.0185 & 0.9853 \\ \text { Age } & 1.4448 & 0.3160 & 4.5717 & 0.0000 \\ \text { Manager } & - 22.5761 & 11.3488 & - 1.9893 & 0.0541 \\ \hline \end{array} \end{array}\] -Referring to Instruction 13-16 Model 1,which of the following is a correct statement?

A) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,after adjusting for the level of significance. B) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,after adjusting for the number of predictors and sample size. C) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,holding constant the effect of all the independent variables. D) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager. A) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,after adjusting for the level of significance. B) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,after adjusting for the number of predictors and sample size. C) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager,holding constant the effect of all the independent variables. D) 49.49% of the total variation in the number of weeks a worker is unemployed due to a layoff can be explained by the age of the worker,the number of years of education received,the number of years at the previous job,marital status,whether the worker is the head of household,and whether the worker is a manager.

Instruction 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression. SUMMARY Regression Statistics \begin{tabular} { l r } Multiple $\mathrm { R }$ & $0.830$ \\ \hline Square & $0.689$ \end{tabular} R Square $\quad 0.689$ Adj. R Square $\quad 0.662$ Std. Error $\quad 17501.643$ Observations 26 ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Siguif } \boldsymbol { F } \\ \text { Regression } & 2 & 15579777040 & 7789888520 & 25.432 & 0.0001 \\ \text { Residual } & 23 & 7045072780 & 306307512 & & \\ \text { Total } & 25 & 22624849820 & & & \end{array}$ $\begin{array} { l l l l l } & \text { Coeff } & \text { StdError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-value } \\ \text { Intercept } & 15800.0000 & 6038.2999 & 2.617 & 0.0154 \\ \text { Capital } & 0.1245 & 0.2045 & 0.609 & 0.5485 \\ \text { Wages } & 7.0762 & 1.4729 & 4.804 & 0.0001 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-5,which of the independent variables in the model are significant at the 5% level?

A) Capital,Wages. B) Wages. C) Capital. D) None of the above. A) Capital,Wages. B) Wages. C) Capital. D) None of the above.

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 value of the F statistic for testing the significance of the entire regression is ________.

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

Instruction 13-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter,a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (XS1U1B11S1U1B0),the amount of insulation in cm (XS1U1B12S1U1B0),the number of windows in the house (XS1U1B13S1U1B0),and the age of the furnace in years (XS1U1B14S1U1B0).Given below are the Microsoft Excel outputs of two regression models. $\begin{array}{lr} {\text { Model 1 }} \\ \hline {\text { Regression Statistics }} \\ \hline \text { R Square } & 0.8080 \\ \text { Adjusted R Square } & 0.7568 \\ \text { Observations } & 20 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrrr} \hline & d f & & S S & M S & F & \text { Significance } F \\ \hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 \mathrm{E}-05 \\ \text { Residual } & 15 & 40262.3259 & 2684.155 & & \\ \text { Total } & 19 & 209765.75 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \text { Standard Error } & {t \text { Stat }} & {\text { P-value }} & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\ \hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05 & 284.9327 & 557.9227 \\ \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \end{array}$ $\begin{array}{l} \text { Model } 2\\ \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { R Square } & 0.7768 \\ \text { Adjusted R } & \\ \text { Square } & 0.7506 \\ \text { Observations } & 20 \\ \hline \end{array} \end{array}$ ANOVA $\begin{array}{lrrrrrr} & d f & &{\text { SS }} & M S & F & \text { Significance } F \\ \hline \text { Regression } & & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text { Residual } & 17 & 46807.5222 & 2753.384 & & \\ \text { Total } & 19 & 209765.75 & & & \\ \hline \end{array}$ $\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 3.17 \mathrm{E}-09 & 396.5273 & 582.1180 \\ \mathrm{X}_{1} \text { (Temperature) } & -5.1103 & 0.6951 & -7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\ \mathrm{X}_{2} \text { (Insulation) } & -14.7195 & 4.8864 & -3.0123 & 0.0078 & -25.0290 & -4.4099 \end{array}$ -Referring to Instruction 13-6 and allowing for a 1% probability of committing a Type I error,what is the decision and conclusion for the test H0: ?1 = ?2 = ?3 = ?4 = 0 vs.H1: At least one ?j ? 0,j = 1,2,... ,4 using Model 1?

A) Reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs. B) Do not reject H0 and conclude that the four independent variables have significant individual linear effects on heating costs. C) Reject H0 and conclude that the four independent variables taken as a group have significant linear effects on average heating costs. D) Do not reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs. A) Reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs. B) Do not reject H0 and conclude that the four independent variables have significant individual linear effects on heating costs. C) Reject H0 and conclude that the four independent variables taken as a group have significant linear effects on average heating costs. D) Do not reject H0 and conclude that the four independent variables taken as a group do not have significant linear effects on heating costs.

Instruction 13-11 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 + 5XS1U1B11S1U1B0 + 8XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = mortgage rate in % XS1U1B12S1U1B0 = 1 if Sydney,0 if Melbourne Y = demand in $100 per capita -Referring to Instruction 13-11,the fitted model for predicting demand in Sydney is ________.

A) 10 + 5X1 B) 10 + 13X1 C) 18 + 5X1 D) 15 + 8X2 A) 10 + 5X1 B) 10 + 13X1 C) 18 + 5X1 D) 15 + 8X2

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 $\begin{array}{llllll} & d f & \text { SS } & \text { MS } & \text { F } & \text { Siguif } \boldsymbol{F} \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array}{lllll} & \text { Coeff } & \text { SttError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \\ \text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-4,what fraction of the variability in house size is explained by income,size of family,and education?

A) 74.8% B) 33.4% C) 27.0% D) 86.5% A) 74.8% B) 33.4% C) 27.0% D) 86.5%

Exam 13: Introduction to Multiple Regression

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 1% level of significance if all you have is the information of the 95% confidence interval estimate for ?₂.

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Question 101

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 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 102

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,which of the following is the correct null hypothesis to determine whether there is a significant relationship between the number of weeks a worker is unemployed due to a layoff and the entire set of explanatory variables?

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Question 103

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 Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff SttError 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,what are the regression degrees of freedom that are missing from the output?

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Question 104

If a categorical independent variable contains 2 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.

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Question 105

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,which of the following is a correct statement?

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Question 106

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 t Stat P-value Lower 99.0\% Upper 99.0\% Intercept Error AGE 123.80 48.71 2.54 0.03 -27.47 275.07 TICKETS -0.82 0.87 -0.95 0.36 -3.51 1.87 DENSITY 21.25 10.66 1.99 0.07 -11.86 54.37 -3.14 6.46 -0.49 0.64 -23.19 16.91 -Referring to Instruction 13-8,the multiple regression model is significant at a 10% level of significance.

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Question 107

Instruction 13-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression. SUMMARY Regression Statistics \begin{tabular} { l r } Multiple $\mathrm { R }$ & $0.830$ \\ \hline Square & $0.689$ \end{tabular} R Square $\quad 0.689$ Adj. R Square $\quad 0.662$ Std. Error $\quad 17501.643$ Observations 26 ANOVA SS MS Siguif Regression 2 15579777040 7789888520 25.432 0.0001 Residual 23 7045072780 306307512 Total 25 22624849820 Coeff StdError Stat -value Intercept 15800.0000 6038.2999 2.617 0.0154 Capital 0.1245 0.2045 0.609 0.5485 Wages 7.0762 1.4729 4.804 0.0001 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-5,which of the independent variables in the model are significant at the 5% level?

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Question 108

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 value of the F statistic for testing the significance of the entire regression is ________.

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Question 109

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,there is sufficient evidence that all of the explanatory variables are related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

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Question 110

Instruction 13-6 One of the most common questions of prospective house buyers pertains to the average cost of heating in dollars (Y). To provide its customers with information on that matter,a large real estate firm used the following 4 variables to predict heating costs: the daily minimum outside temperature in degrees of Celsius (X₁),the amount of insulation in cm (X₂),the number of windows in the house (X₃),and the age of the furnace in years (X₄).Given below are the Microsoft Excel outputs of two regression models. Model 1 Regression Statistics R Square 0.8080 Adjusted R Square 0.7568 Observations 20 ANOVA df SS MS F Significance F Regression 4 169503.4241 42375.86 15.7874 2.96869-05 Residual 15 40262.3259 2684.155 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 90.0\% Upper 90.0\% Intercept 421.4277 77.8614 5.4125 7.2-05 284.9327 557.9227 (Temperature) -4.5098 0.8129 -5.5476 5.58-05 -5.9349 -3.0847 (Insulation) -14.9029 5.0508 -2.9505 0.0099 -23.7573 -6.0485 (Windows) 0.2151 4.8675 0.0442 0.9653 -8.3181 8.7484 (Furnace Age) 6.3780 4.1026 1.5546 0.1408 -0.8140 13.5702 Model 2 Regression Statistics R Square 0.7768 Adjusted R Square 0.7506 Observations 20 ANOVA df SS MS F Significance F Regression 2 162958.2277 81479.11 29.5923 2.9036-06 Residual 17 46807.5222 2753.384 Total 19 209765.75 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept 489.3227 43.9826 11.1253 3.17-09 396.5273 582.1180 (Temperature) -5.1103 0.6951 -7.3515 1.13-06 -6.5769 -3.6437 (Insulation) -14.7195 4.8864 -3.0123 0.0078 -25.0290 -4.4099 -Referring to Instruction 13-6 and allowing for a 1% probability of committing a Type I error,what is the decision and conclusion for the test H₀: ?₁ = ?₂ = ?₃ = ?₄ = 0 vs.H₁: At least one ?_j ? 0,j = 1,2,... ,4 using Model 1?

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Question 111

Instruction 13-7 You decide to predict petrol prices in different cities and towns in Australia for your term project.Your dependent variable is price of petrol per litre and your explanatory variables are per capita income,the number of firms that manufacture automobile parts in and around the city,the number of new business starts in the last year,population density of the city,percentage of local taxes on petrol,and the number of people using public transportation.You collected data of 32 cities and obtained a regression sum of squares SSR = 122.8821.Your computed value of standard error of the estimate is 1.9549. -Referring to Instruction 13-7,what is the value of the coefficient of multiple determination?

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Question 112

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 value of the test statistic is ________.

(Short Answer)

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Question 113

When an additional explanatory variable is introduced into a multiple regression model,the adjusted r² can never decrease.

(True/False)

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Question 114

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,you can conclude that mean teacher salary has no impact on mean percentage of students passing the proficiency test at a 10% level of significance based solely on the 95% confidence interval estimate for ?₂.

(True/False)

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Question 115

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,there is sufficient evidence that the percentage of students passing the proficiency test depends on at least one of the explanatory variables.

(True/False)

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Question 116

The denominator degrees of freedom for the partial F statistic are

(Multiple Choice)

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Question 117

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,the null hypothesis H₀: ?₁ = ?₂ = ?₃= 0 implies that percentage of students passing the proficiency test is not affected by some of the explanatory variables.

(True/False)

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Question 118

Instruction 13-11 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 + 5X₁ + 8X₂ where X₁ = mortgage rate in % X₂ = 1 if Sydney,0 if Melbourne Y = demand in $100 per capita -Referring to Instruction 13-11,the fitted model for predicting demand in Sydney is ________.

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Question 119

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 Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff SttError 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,what fraction of the variability in house size is explained by income,size of family,and education?

(Multiple Choice)

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Question 120

If a categorical independent variable contains 2 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.

When an additional explanatory variable is introduced into a multiple regression model,the adjusted r² can never decrease.

The denominator degrees of freedom for the partial F statistic are

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

Filters

Exam 13: Introduction to Multiple Regression

If a categorical independent variable contains 2 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.

When an additional explanatory variable is introduced into a multiple regression model,the adjusted r2 can never decrease.

The denominator degrees of freedom for the partial F statistic are

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

Filters

When an additional explanatory variable is introduced into a multiple regression model,the adjusted r² can never decrease.