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: 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 $\begin{array}{llllll} & d f & \text { SS } & \text { MS } & \text { F } & \text { Signif } F \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array}{lllll} & \text { Coeff } & \text { StdError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \\ \text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-4,what minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square metre home (House = 50)?

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

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,what is the experimental unit for this analysis?

A) A client on a weight-loss program. B) A month. C) A morning,afternoon,or evening session. D) A clinic. A) A client on a weight-loss program. B) A month. C) A morning,afternoon,or evening session. D) A clinic.

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,what can you say about Model 1?

A) The model explains 80.8% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 75.7% of the sample variability of heating costs. B) The model explains 77.7% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 75.1% of the sample variability of heating costs. C) The model explains 75.7% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 80.8% of the sample variability of heating costs. D) The model explains 75.1% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 77.7% of the sample variability of heating costs. A) The model explains 80.8% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 75.7% of the sample variability of heating costs. B) The model explains 77.7% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 75.1% of the sample variability of heating costs. C) The model explains 75.7% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 80.8% of the sample variability of heating costs. D) The model explains 75.1% of the sample variability of heating costs;after correcting for the degrees of freedom,the model explains 77.7% of the sample variability of heating costs.

The coefficient of multiple determination r2Y.12

A) measures the proportion of variation in Y that is explained by X1 and X2. B) measures the proportion of variation in Y that is explained by X1 holding X2 constant. C) will have the same sign as b1. D) measures the variation around the predicted regression equation. A) measures the proportion of variation in Y that is explained by X1 and X2. B) measures the proportion of variation in Y that is explained by X1 holding X2 constant. C) will have the same sign as b1. D) measures the variation around the predicted regression equation.

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,which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

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

Instruction 13-16 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,which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

A) H1: ?1 ? 0 B) H1: ?2 ? 0 C) H1: ?4 ? 0 D) H1: ?3 ? 0 A) H1: ?1 ? 0 B) H1: ?2 ? 0 C) H1: ?4 ? 0 D) H1: ?3 ? 0

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 numerator and denominator degrees of freedom,respectively,for the test statistic 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?

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

Instruction 13-12 An automotive engineer would like to be able to predict automobile fuel economy.She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6)of a car.She believes that the appropriate model is Y = 40 - 0.05XS1U1B11S1U1B0 + 20XS1U1B12S1U1B0 - 0.1XS1U1B11S1U1B0XS1U1B12S1U1B0 where XS1U1B11S1U1B0 = engine power XS1U1B12S1U1B0 = 1 if 4 cylinders,0 if 6 cylinders Y = economy expressed as kilometres. -Referring to Instruction 13-12,the predicted number of kilometres for a 300 engine power,6-cylinder car is ________.

The answer of Instruction 13-12 An automotive engineer would like to...

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,in terms of the ?'s in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X1)when attending the afternoon session.

A) ?1 + ?4 B) ?1 + ?5 C) ?1 D) ?4 + ?5 A) ?1 + ?4 B) ?1 + ?5 C) ?1 D) ?4 + ?5

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 residual degrees of freedom that are missing from the output?

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

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 estimated average consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

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

Instruction 13-16 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 $\begin{array}{lrrrrr} & D f & S S & M S &{\text { SS }} &{\text { Significance F }} \\ \text { Regression } & 6 & 11048.6415 & 1841.4402 & 5.3885 & 0.00057 \\ \text { Residual } & 33 & 11277.2586 & 341.7351 & & \\ \text { Total } & 39 & 22325.9 & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 32.6595 & 23.18302 & 1.4088 & 0.1683 & -14.5067 & 79.8257 \\ \text { Age } & 1.2915 & 0.3599 & 3.5883 & 0.0011 & 0.5592 & 2.0238 \\ \text { Edu } & -1.3537 & 1.1766 & -1.1504 & 0.2582 & -3.7476 & 1.0402 \\ \text { Job Yr } & 0.6171 & 0.5940 & 1.0389 & 0.3064 & -0.5914 & 1.8257 \\ \text { Married } & -5.2189 & 7.6068 & -0.6861 & 0.4974 & -20.6950 & 10.2571 \\ \text { Head } & -14.2978 & 7.6479 & -1.8695 & 0.0704 & -29.8575 & 1.2618 \\ \text { Manager } & -24.8203 & 11.6932 & -2.1226 & 0.0414 & -48.6102 & -1.0303 \\ \hline \end{array}$ 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,predict the number of weeks being unemployed due to a layoff for a worker who is a 30 year old,has 10 years of education,has 15 years of experience at the previous job,is married,is the head of household,and is a manager.

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: SUMMARY Regression Statistics Multiple R 0.865 R Square 0.748 Adj. R Square 0.726 Std. Error 5.195 Observations 50 ANOVA df SS MS F Signif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff StdError 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 minimum annual income would an individual with a family size of 9 and 10 years of education need to attain a predicted 5,000 square metre home (House = 50)?

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Question 141

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 test H₀: β₁ = β₂ = 0.The appropriate alternative hypothesis is ________.

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Question 142

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 estimate of the unit change in the mean of Y per unit change in X₄,taking into account the effects of the other three variables,is ________.

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Question 143

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,what is the experimental unit for this analysis?

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Question 144

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,what can you say about Model 1?

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Question 145

The slopes in a multiple regression model are called net regression coefficients.

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Question 146

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,there is a difference in the mean number of weeks a worker is unemployed due to a layoff between a worker who is married and one who is not at a 5% level of significance if you use only the information of the 95% confidence interval estimate for ?₄.

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Question 147

The coefficient of multiple determination r²_Y_.12

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Question 148

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,which of the following is the correct null hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

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Question 149

In a particular model,the sum of the squared residuals was 847.If the model had 5 independent variables,and the data set contained 40 points,the value of the standard error of the estimate is 24.911.

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Question 150

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,which of the following is the correct alternative hypothesis to test whether age has any effect on the number of weeks a worker is unemployed due to a layoff,while holding constant the effect of all the other independent variables?

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Question 151

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 instructional spending per pupil has no impact on mean percentage of students passing the proficiency test at a 5% level of significance using the 95% confidence interval estimate for ?₃.

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Question 152

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 numerator and denominator degrees of freedom,respectively,for the test statistic 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 153

Instruction 13-12 An automotive engineer would like to be able to predict automobile fuel economy.She believes that the two most important characteristics that affect economy are engine power and the number of cylinders (4 or 6)of a car.She believes that the appropriate model is Y = 40 - 0.05X₁ + 20X₂ - 0.1X₁X₂ where X₁ = engine power X₂ = 1 if 4 cylinders,0 if 6 cylinders Y = economy expressed as kilometres. -Referring to Instruction 13-12,the predicted number of kilometres for a 300 engine power,6-cylinder car is ________.

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Question 154

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 coefficient of multiple determination,r²_Y.1234,is ________.

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Question 155

The coefficient of multiple determination r² measures the proportion of variation in Y that is explained by X₁ and X₂.

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Question 156

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,in terms of the ?'s in the model,give the mean change in weight-loss (Y)for every 1 month increase in time in the program (X₁)when attending the afternoon session.

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Question 157

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 residual degrees of freedom that are missing from the output?

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Question 158

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 estimated average consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

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Question 159

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 SS 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,predict the number of weeks being unemployed due to a layoff for a worker who is a 30 year old,has 10 years of education,has 15 years of experience at the previous job,is married,is the head of household,and is a manager.

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Question 160

The slopes in a multiple regression model are called net regression coefficients.

The coefficient of multiple determination r²_Y_.12

In a particular model,the sum of the squared residuals was 847.If the model had 5 independent variables,and the data set contained 40 points,the value of the standard error of the estimate is 24.911.

The coefficient of multiple determination r² measures the proportion of variation in Y that is explained by X₁ and X₂.

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

The slopes in a multiple regression model are called net regression coefficients.

The coefficient of multiple determination r2Y.12

In a particular model,the sum of the squared residuals was 847.If the model had 5 independent variables,and the data set contained 40 points,the value of the standard error of the estimate is 24.911.

The coefficient of multiple determination r2 measures the proportion of variation in Y that is explained by X1 and X2.

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

The coefficient of multiple determination r²_Y_.12

The coefficient of multiple determination r² measures the proportion of variation in Y that is explained by X₁ and X₂.