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) 40.30% 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. B) 40.30% 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. C) 40.30% 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. D) 40.30% 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. A) 40.30% 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. B) 40.30% 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. C) 40.30% 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. D) 40.30% 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.

Instruction 13-13 The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily average of the percentage of students attending class (% Attendance),average teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, XS1U1B11S1U1B0 = % Attendance,XS1U1B12 S1U1B0= Salaries and XS1U1B13 S1U1B0= Spending: $\begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { Multiple R } & 0.7930 \\ \text { R Square } & 0.6288 \\ \text { Adjusted R } & 0.6029 \\ \text { Square } & \\ \text { Standard } & 10.4570 \\ \text { Error } & \\ \text { Observations } & 47 \\ \hline \end{array}$ ANOVA $\begin{array}{lrrrrr} \hline & d f & {\text { SS }} & M S & F & \text { Significance } F \\ \text { Regression } & 3 & 7965.08 & 2655.03 & 24.2802 & 0.0000 \\ \text { Residual } & 43 & 4702.02 & 109.35 & & \\ \text { Total } & 46 & 12667.11 & & & \end{array}$ $\begin{array}{lrrrrrrr} \hline & \text { Coefficients } & \begin{array}{c} \text { Standard } \\ \text { Error } \end{array} & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & -753.4225 & 101.1149 & -7.4511 & 0.0000 & -957.3401 & -549.5050 \\ \text { \% Attendance } & 8.5014 & 1.0771 & 7.8929 & 0.0000 & 6.3292 & 10.6735 \\ \text { Salary } & 0.000000685 & 0.0006 & 0.0011 & 0.9991 & -0.0013 & 0.0013 \\ \text { Spending } & 0.0060 & 0.0046 & 1.2879 & 0.2047 & -0.0034 & 0.0153 \end{array}$ -Referring to Instruction 13-13,which of the following is the correct null hypothesis to test whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

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

Instruction 13-1 A manager of a product sales group believes the number of sales made by an employee (Y)depends on how many years that employee has been with the company (XS1U1B11S1U1B0)and how he/she scored on a business aptitude test (XS1U1B12S1U1B0).A random sample of 8 employees provides the following: \[\begin{array} { | l | l | l | l | } \hline \text { Employee } & \text { Y } & \text { XI } & \text { X2 } \\ \hline 1 & 100 & 10 & 7 \\ \hline 2 & 90 & 3 & 10 \\ \hline 3 & 80 & 8 & 9 \\ \hline 4 & 70 & 5 & 4 \\ \hline 5 & 60 & 5 & 8 \\ \hline 6 & 50 & 7 & 5 \\ \hline 7 & 40 & 1 & 4 \\ \hline 8 & 30 & 1 & 1 \\ \hline \end{array}\] -Referring to Instruction 13-1,for these data,what is the estimated coefficient for the variable representing years an employee has been with the company,b1?

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

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

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

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

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

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 fitted model for predicting economy for 6-cylinder cars is ________.

A) 60 - 0.10X1 B) 40 - 0.10X1 C) 40 - 0.05X1 D) 60 - 0.15X1 A) 60 - 0.10X1 B) 40 - 0.10X1 C) 40 - 0.05X1 D) 60 - 0.15X1

Instruction 13-4 A real estate builder wishes to determine how house size (House)is influenced by family income (Income),family size (Size),and education of the head of household (School).House size is measured in hundreds of square metres,income is measured in thousands of dollars,and education is in years.The builder randomly selected 50 families and ran the multiple regression.Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics $ \begin{array}{ll}\text { Multiple R } & 0.865 \\ \text { R Square } & 0.748 \\ \text { Adj. R Square } & 0.726 \\ \text { Std. Error } & 5.195 \\ \text { Observations } & 50\end{array} $ ANOVA $\begin{array}{llllll} & d f & \text { SS } & \text { MS } & F & \text { Siguif } F \\ \text { Regression } & & 3605.7736 & 901.4434 & & 0.0001 \\ \text { Residual } & & 1214.2264 & 26.9828 & & \\ \text { Total } & 49 & 4820.0000 & & & \end{array}$ $\begin{array}{lllll} & \text { Coeff } & \text { StdError } & \boldsymbol{t} \text { Stat } & \boldsymbol{P} \text {-value } \\ \text { Intercept } & -1.6335 & 5.8078 & -0.281 & 0.7798 \\ \text { Income } & 0.4485 & 0.1137 & 3.9545 & 0.0003 \\ \text { Size } & 4.2615 & 0.8062 & 5.286 & 0.0001 \\ \text { School } & -0.6517 & 0.4319 & -1.509 & 0.1383 \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-4,one individual in the sample had an annual income of $10,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square metre (House = 10.00).What is the residual (in hundreds of square metre)for this data point?

A) 8.10 B) -8.10 C) 5.40 D) -5.40 A) 8.10 B) -8.10 C) 5.40 D) -5.40

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,what is the p-value for Wages?

A) 0.05 B) 0.01 C) 0.0001 D) None of the above. A) 0.05 B) 0.01 C) 0.0001 D) None of the above.

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 Multiple R $\quad 0.830$ R Square $\quad 0.689$ Adj. R Square $\quad 0.662$ Std. Error $\quad 17501.643$ Observations $\quad26$ 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,what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?

A) 20,455.98 B) 17,277.49 C) 16,520.07 D) 15,800.00 A) 20,455.98 B) 17,277.49 C) 16,520.07 D) 15,800.00

Instruction 13-3 An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. SUMMARY Regression Statistics $\begin{array} { l l } \text { Multiple R } & 0.991 \\ \text { R Square } & 0.982 \\ \text { Adj. R Square } & 0.976 \\ \text { Std. Error } & 0.299 \\ \text { Observations } & 10 \end{array}$ ANOVA $\begin{array} { l l l l l l } & \boldsymbol { d f } & \text { SS } & \text { MS } & \boldsymbol { F } & \text { Signiff } \\ \text { Regression } & 2 & 33.4163 & 16.7082 & 186.325 & 0.0001 \\ \text { Residual } & 7 & 0.6277 & 0.0897 & & \\ \text { Total } & 9 & 34.0440 & & & \\ & & & & & \\ & \text { Coeff } & \text { StaError } & \boldsymbol { t } \text { Stat } & \boldsymbol { P } \text {-Value } & \\ \text { Intercept } & - 1.6335 & 0.5674 & - 0.152 & 0.8837 & \\ \text { GDP } & 0.7654 & 0.0574 & 13.340 & 0.0001 & \\ \text { Price } & - 0.0006 & 0.0028 & - 0.219 & 0.8330 & \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-3,to test whether aggregate price index has a positive impact on consumption,the p-value is

A) 0.4165. B) 0.0001. C) 0.8330. D) 0.5835. A) 0.4165. B) 0.0001. C) 0.8330. D) 0.5835.

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. $\begin{array}{lr} {\text { Model 1 }} \\ \hline{\text { Regression Statistics }} \\ \hline \text { R Square } & 0.8080 \\ \text { Adjusted R Square } & 0.7568 \\ \text { Observations } & 20 \end{array}$ ANOVA $\begin{array}{lrrrrr} & d f & {\text { SS }} & M S & F & \text { Significance } F \\ \hline \text { Regression } & 4 & 169503.4241 & 42375.86 & 15.7874 & 2.96869 \mathrm{E}-05 \\ \text { Residual } & 15 & 40262.3259 & 2684.155 & & \\ \text { Total } & 19 & 209765.75 & & \end{array}$ $\begin{array}{lrrrrrrr} & \text { Coefficients } & \text { Standard Error } &{\text { t Stat }} & \text { P-value } & \text { Lower 90.0\% } & \text { Upper 90.0\% } \\ \hline \text { Intercept } & 421.4277 & 77.8614 & 5.4125 & 7.2 \mathrm{E}-05 & 284.9327 & 557.9227 \\ \mathrm{X}_{1} \text { (Temperature) } & -4.5098 & 0.8129 & -5.5476 & 5.58 \mathrm{E}-05 & -5.9349 & -3.0847 \\ \mathrm{X}_{2} \text { (Insulation) } & -14.9029 & 5.0508 & -2.9505 & 0.0099 & -23.7573 & -6.0485 \\ \mathrm{X}_{3} \text { (Windows) } & 0.2151 & 4.8675 & 0.0442 & 0.9653 & -8.3181 & 8.7484 \\ \mathrm{X}_{4} \text { (Furnace Age) } & 6.3780 & 4.1026 & 1.5546 & 0.1408 & -0.8140 & 13.5702 \end{array}$ $\begin{array}{l} \text { Model } 2\\ \begin{array}{lr} \hline {\text { Regression Statistics }} \\ \hline \text { R Square } & 0.7768 \\ \text { Adjusted R } & \\ \text { Square } & 0.7506 \\ \text { Observations } & 20 \\ \hline \end{array} \end{array}$ ANOVA $\begin{array}{lrrrrrr} \hline & d f & {\text { SS }} & M S & F & \text { Significance } F \\ \hline \text { Regression } & 2 & 162958.2277 & 81479.11 & 29.5923 & 2.9036 \mathrm{E}-06 \\ \text { Residual } & 17 & 46807.5222 & 2753.384 & & \\ \text { Total } & 19 & 209765.75 & & \end{array}$ $\begin{array}{lrrrrrr} & \text { Coefficients } & \text { Standard Error } & \text { tStat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\ \hline \text { Intercept } & 489.3227 & 43.9826 & 11.1253 & 3.17 \mathrm{E}-09 & 396.5273 & 582.1180 \\ \mathrm{X}_{1} \text { (Temperature) } & -5.1103 & 0.6951 & -7.3515 & 1.13 \mathrm{E}-06 & -6.5769 & -3.6437 \\ \mathrm{X}_{2} \text { (Insulation) } & -14.7195 & 4.8864 & -3.0123 & 0.0078 & -25.0290 & -4.4099 \end{array}$ -Referring to Instruction 13-6,what is your decision and conclusion for the test H0: ?2 = 0 vs.H1: ?2 < 0 at the ? = 0.01 level of significance using Model 1?

A) Reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs. B) Reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs. C) Do not reject H0 and conclude that the amount of insulation has a linear effect on heating cots. D) Do not reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs. A) Reject H0 and conclude that the amount of insulation does not have a linear effect on heating costs. B) Reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs. C) Do not reject H0 and conclude that the amount of insulation has a linear effect on heating cots. D) Do not reject H0 and conclude that the amount of insulation has a negative linear effect on heating costs.

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,the null hypothesis H₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅ = ?₆ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by some of the explanatory variables.

(True/False)

4.9/5

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Question 181

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: OUTPUT SUMMARY Regression Statistics Multiple R 0.916 R Square 0.839 Adj. R Square 0.732 Std. Error 0.24685 Observations 6 ANOVA df SS MS F Siguif F Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StDError Stat P-Value Intercept 4.593897 1.13374542 4.052 0.0271 GDP -0.247270 0.06268485 -3.945 0.0290 Price 0.001443 0.00101241 1.425 0.2494 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-14,the Head of Department wants to use a t test to test for the significance of the coefficient of X₁.At a level of significance of 0.05,the department head would decide that ?₁ ? 0.

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Question 182

Instruction 13-13 The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily average of the percentage of students attending class (% Attendance),average teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance,X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA df SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Instruction 13-13,what is the standard error of estimate?

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Question 183

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 184

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 should be rejected at a 5% level of significance when testing whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of explanatory variables.

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Question 185

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 all of the explanatory variables.

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Question 186

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,the null hypothesis H₀: ?₁ = ?₂ = ?₃ = ?₄ = ?₅ = ?₆ = 0 implies that the number of weeks a worker is unemployed due to a layoff is not affected by any of the explanatory variables.

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Question 187

Instruction 13-13 The education department's regional executive officer wanted to predict the percentage of students passing a Grade 6 proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily average of the percentage of students attending class (% Attendance),average teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable, X₁ = % Attendance,X₂= Salaries and X₃= Spending: Regression Statistics Multiple R 0.7930 R Square 0.6288 Adjusted R 0.6029 Square Standard 10.4570 Error Observations 47 ANOVA df SS MS F Significance F Regression 3 7965.08 2655.03 24.2802 0.0000 Residual 43 4702.02 109.35 Total 46 12667.11 Coefficients Standard Error t Stat P-value Lower 95\% Upper 95\% Intercept -753.4225 101.1149 -7.4511 0.0000 -957.3401 -549.5050 \% Attendance 8.5014 1.0771 7.8929 0.0000 6.3292 10.6735 Salary 0.000000685 0.0006 0.0011 0.9991 -0.0013 0.0013 Spending 0.0060 0.0046 1.2879 0.2047 -0.0034 0.0153 -Referring to Instruction 13-13,which of the following is the correct null hypothesis to test whether daily mean of the percentage of students attending class has any effect on percentage of students passing the proficiency test,taking into account the effect of all the other independent variables?

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Question 188

When an explanatory variable is dropped from a multiple regression model,the coefficient of multiple determination can increase.

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Question 189

Instruction 13-14 The Head of the Accounting Department wanted to see if she could predict the average grade of students using the number of course units (credits)and total university entrance exam scores of each.She takes a sample of students and generates the following Microsoft Excel output: SUMMARY Regression Statistics Multiple R 0.916 R Square 0.839 Adj. R Square 0.732 Std. Error 0.24685 Observations 6 ANOVA SS MS Signif Regression 2 0.95219 0.47610 7.813 0.0646 Residual 3 0.18281 0.06094 Total 5 1.13500 Coeff StdError Stat -Value Intercept 4.593897 1.13374542 4.052 0.0271 GDP -0.247270 0.06268485 -3.945 0.0290 Price 0.001443 0.00101241 1.425 0.2494 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-14,the Head of Department wants to use a t test to test for the significance of the coefficient of X₁.The value of the test statistic is ________.

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Question 190

Instruction 13-1 A manager of a product sales group believes the number of sales made by an employee (Y)depends on how many years that employee has been with the company (X₁)and how he/she scored on a business aptitude test (X₂).A random sample of 8 employees provides the following: Employee Y XI X2 1 100 10 7 2 90 3 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 1 4 8 30 1 1 -Referring to Instruction 13-1,for these data,what is the estimated coefficient for the variable representing years an employee has been with the company,b₁?

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Question 191

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

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Question 192

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

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Question 193

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 fitted model for predicting economy for 6-cylinder cars is ________.

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Question 194

Instruction 13-4 A real estate builder wishes to determine how house size (House)is influenced by family income (Income),family size (Size),and education of the head of household (School).House size is measured in hundreds of square metres,income is measured in thousands of dollars,and education is in years.The builder randomly selected 50 families and ran the multiple regression.Microsoft Excel output is provided below: OUTPUT SUMMARY Regression Statistics Multiple R 0.865 R Square 0.748 Adj. R Square 0.726 Std. Error 5.195 Observations 50 ANOVA df SS MS F Siguif F Regression 3605.7736 901.4434 0.0001 Residual 1214.2264 26.9828 Total 49 4820.0000 Coeff StdError Stat -value Intercept -1.6335 5.8078 -0.281 0.7798 Income 0.4485 0.1137 3.9545 0.0003 Size 4.2615 0.8062 5.286 0.0001 School -0.6517 0.4319 -1.509 0.1383 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-4,one individual in the sample had an annual income of $10,000,a family size of 1,and an education of 8 years.This individual owned a home with an area of 1,000 square metre (House = 10.00).What is the residual (in hundreds of square metre)for this data point?

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Question 195

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,what is the p-value for Wages?

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Question 196

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 Multiple R $\quad 0.830$ R Square $\quad 0.689$ Adj. R Square $\quad 0.662$ Std. Error $\quad 17501.643$ Observations $\quad26$ 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,what are the predicted sales (in millions of dollars)for a company spending $100 million on capital and $100 million on wages?

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Question 197

Instruction 13-3 An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. SUMMARY Regression Statistics Multiple R 0.991 R Square 0.982 Adj. R Square 0.976 Std. Error 0.299 Observations 10 ANOVA SS MS Signiff Regression 2 33.4163 16.7082 186.325 0.0001 Residual 7 0.6277 0.0897 Total 9 34.0440 Coeff StaError Stat -Value Intercept -1.6335 0.5674 -0.152 0.8837 GDP 0.7654 0.0574 13.340 0.0001 Price -0.0006 0.0028 -0.219 0.8330 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 13-3,to test whether aggregate price index has a positive impact on consumption,the p-value is

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Question 198

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 tStat 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 is your decision and conclusion for the test H₀: ?₂ = 0 vs.H₁: ?₂ < 0 at the ? = 0.01 level of significance using Model 1?

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Question 199

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,holding constant the effect of city,each additional increase of 1% in the mortgage rate would lead to an estimated increase of ________ per capita in the mean demand.

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Question 200

When an explanatory variable is dropped from a multiple regression model,the coefficient of multiple determination can increase.

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Basic Probability

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

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