As a project for his business statistics class,a student examined the factors that determined parking metre rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesised is Yi = α + β1x1i + β2x2i + β3x3i + εi Where Y is the metre price X1 is the number of blocks to the quad X2 is a dummy variable that takes the value 1 if the metre is located in downtown And off campus and the value 0 otherwise X3 is a dummy variable that takes the value 1 if the metre is located outside of Downtown and off campus,and the value 0 otherwise Suppose that whether the metre is located on campus is an important explanatory factor.Why should the variable that depicts this attribute not be included in the model?

A) Its inclusion will introduce autocorrelation. B) Its inclusion will inflate the standard errors of the estimated coefficients. C) Its inclusion will introduce collinearity. D) Both B and C. A) Its inclusion will introduce autocorrelation. B) Its inclusion will inflate the standard errors of the estimated coefficients. C) Its inclusion will introduce collinearity. D) Both B and C.

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. $\begin{array}{l|l|l|l|l|l|} \text { SUMMARY } & output& \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.747 \\ \hline \text { R Square } & & 0.558 \\ \hline \text { Adj. R Square } & & 0.478 \\ \hline \text { Std. Error } & 363.1 \\ \hline \text { Observations } & 14 \\\hline\\ \hline \text { ANOVA } & & & & & \\ \hline & \text { df } & \text { SS } & \text { MS } & F & \text { Signưf } F \\ \hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\ \hline \text { Residual } & 11 & 8193929 & 744903 & & \\ \hline \text { Total } & 13 & 18538726 & & & \\\hline\\ \hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\ \hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\ \hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\ \hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\ \hline \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic curvilinear relationship between time and dose.The value of the test statistic is ________.

The answer of Instruction 16-5 A chemist employed by a pharmaceutical...

Instruction 16-2 A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0X + βS1U1B12S1U1B0XS1U1P12S1S1P0S1U1P1 S1S1P0+S1U1P1 S1S1P0S1U1P1εS1S1P0 where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: $\begin{array}{l|l|l|l|l|l|} \hline \text { SUMMARY } & & \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.994 \\ \hline \text { R Square } & & 0.988 \\ \hline \text { Std. Error } & & 12.42 \\ \hline \text { Observations } & & 12 \\\hline\\ \hline\text { ANOVA }\\ \hline& \text { If } & \text { SS } & \text { MS } & F & \text { Sigưf F } \\ \hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\ \hline \text { Residual } & 9 & 1388 & 154 & & \\ \hline \text { Total } & 11 & 116533 & & & \\\hline\\ \hline& \text { Coeff } & \text { StdError } & \text { Stat } & P \text {-Value } \\ \hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\ \hline \text { Price } & 0.31 & 0.06 & -5.14 & 0.0006 \\ \hline \text { Price Sq } & 0.000067 & 0.00007 & 0.95 & 0.3647\\ \hline \end{array}$ Note: Std.Error = Standard Error -Referring to Instruction 16-2,and noting that this model includes both a linear and a quadratic term,what is the correct interpretation of the coefficient of multiple determination?

A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price. B) 98.8% of the total variation in demand can be explained by the addition of the square term in price. C) 98.8% of the total variation in demand can be explained by just the square term in price. D) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price. A) 98.8% of the total variation in demand can be explained by the linear relationship between demand and price. B) 98.8% of the total variation in demand can be explained by the addition of the square term in price. C) 98.8% of the total variation in demand can be explained by just the square term in price. D) 98.8% of the total variation in demand can be explained by the quadratic relationship between demand and price.

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. $\begin{array}{l|l|l|l|l|l|} \text { SUMMARY } & output& \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.747 \\ \hline \text { R Square } & & 0.558 \\ \hline \text { Adj. R Square } & & 0.478 \\ \hline \text { Std. Error } & 363.1 \\ \hline \text { Observations } & 14 \\\hline\\ \hline \text { ANOVA } & & & & & \\ \hline & \text { df } & \text { SS } & \text { MS } & F & \text { Signưf } F \\ \hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\ \hline \text { Residual } & 11 & 8193929 & 744903 & & \\ \hline \text { Total } & 13 & 18538726 & & & \\\hline\\ \hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\ \hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\ \hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\ \hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\ \hline \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a quadratic model without a linear term and a quadratic model that includes a linear term.The value of the test statistic is ________.

The answer of Instruction 16-5 A chemist employed by a pharmaceutical...

Instruction 16-1 To explain personal consumption (CONS)measured in dollars,data is collected for \[\begin{array}{l} \begin{array} {|l|l|} \hline \text {INC }&\text { personal income in dollars}\\ \hline&\text {$ \$ 1 $ plus the credit limit in dollars available to the }\\ \text { CRDTLIM}&\text { individual}\\ \hline&\text {average annualised percentage interest rate for }\\ \text {APR: }&\text {borrowing for the individual }\\ \hline&\text {per person advertising expenditure in dollars by }\\ &\text { manufacturers in the city where the }\\ \text {ADVT: }&\text {individual lives }\\ \hline\text {GENDER:}&\text {gender of the individual; 1 if female, 0 if male}\\ \hline \end{array} \end{array}\] A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was = 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER -Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for ADVT?

A) A 1% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant. B) A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant. C) A $1 increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant. D) A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant. A) A 1% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant. B) A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant. C) A $1 increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of $2.35 on personal consumption holding other variables constant. D) A 100% increase in per person advertising expenditure by the manufacturer will result in an estimated mean increase of 2.35% on personal consumption holding other variables constant.

Instruction 16-1 To explain personal consumption (CONS)measured in dollars,data is collected for \[\begin{array}{l} \begin{array} {|l|l|} \hline \text {INC }&\text { personal income in dollars}\\ \hline&\text {$ \$ 1 $ plus the credit limit in dollars available to the }\\ \text { CRDTLIM}&\text { individual}\\ \hline&\text {average annualised percentage interest rate for }\\ \text {APR: }&\text {borrowing for the individual }\\ \hline&\text {per person advertising expenditure in dollars by }\\ &\text { manufacturers in the city where the }\\ \text {ADVT: }&\text {individual lives }\\ \hline\text {GENDER:}&\text {gender of the individual; 1 if female, 0 if male}\\ \hline \end{array} \end{array}\] A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was = 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER -Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for APR?

A) A 1% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant. B) A one percentage point increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant. C) A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant. D) A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant. A) A 1% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant. B) A one percentage point increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant. C) A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of $5.77 on personal consumption holding other variables constant. D) A 100% increase in mean annualised percentage interest rate will result in an estimated mean increase of 5.77% on personal consumption holding other variables constant.

Instruction 16-2 A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model: Y = βS1U1B10S1U1B0 + βS1U1B11S1U1B0X + βS1U1B12S1U1B0XS1U1P12S1S1P0S1U1P1 S1S1P0+S1U1P1 S1S1P0S1U1P1εS1S1P0 where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: $\begin{array}{|l|l|l|l|l|l|} \text { SUMMARY } &output & \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.994 \\ \hline \text { R Square } & & 0.988 \\ \hline \text { Std. Error } & & 12.42 \\ \hline \text { Observations } & & 12\\\hline\\ \hline\text { ANOVA }\\ \hline & \text { dff } & \text { SS } & \text { MS } & F & \text { Siguif } F \\ \hline \text { Regression } & 2 & 115145 & 57573 & 373 & 0.0001 \\ \hline \text { Residual } & 9 & 1388 & 154 & & \\ \hline \text { Total } & 11 & 116533 & & &\\\hline\\ \hline & \text { Coeff } & \text { StdError } & \text { t Stat } & \text { P-Value } \\ \hline \text { Intercept } & 286.42 & 9.66 & 29.64 & 0.0001 \\ \hline \text { Price } & -0.31 & 0.06 & -5.14 & 0.0006 \\ \hline\text { Price Sq } & p .000067 & p .00007 & p .95 & p .3647\\\hline \end{array}$ Note: Std.Error = Standard Error -Referring to Instruction 16-2,what is the value of the test statistic for testing whether the quadratic term is necessary in fitting in the response curve relating the demand (Y)and the price (X)?

A) -5.14 B) 0.95 C) 373 D) None of the above. A) -5.14 B) 0.95 C) 373 D) None of the above.

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. $\begin{array}{l|l|l|l|l|l|} \text { SUMMARY } & output& \\ \hline \text { Regression } & \text { Statistics } & \\ \hline \text { Multiple R } & & 0.747 \\ \hline \text { R Square } & & 0.558 \\ \hline \text { Adj. R Square } & & 0.478 \\ \hline \text { Std. Error } & 363.1 \\ \hline \text { Observations } & 14 \\\hline\\ \hline \text { ANOVA } & & & & & \\ \hline & \text { df } & \text { SS } & \text { MS } & F & \text { Signưf } F \\ \hline \text { Regression } & 2 & 10344797 & 5172399 & 6.94 & 0.0110 \\ \hline \text { Residual } & 11 & 8193929 & 744903 & & \\ \hline \text { Total } & 13 & 18538726 & & & \\\hline\\ \hline & \text { Coeff } & \text { StdErior } & \text { Stat } & P \text {-value } \\ \hline \text { Intercept } & 1283.0 & 352.0 & 3.65 & 0.0040 \\ \hline \text { CenDose } & 25.228 & 3.631 & 2.92 & 0.0140 \\ \hline \text { CenDoseSq } & 0.8604 & 0.3722 & 2.31 & 0.0410\\ \hline \end{array}$ Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic relationship between time and dose.The p-value of the test is ________.

The answer of Instruction 16-5 A chemist employed by a pharmaceutical...

Exam 16: Multiple Regression Model Building

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the model that includes X₁,X₂,X₃,X₅ and X₆should be among the appropriate models using the Mallow's C_p statistic.

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Question 1

Correct Answer:

Verified

True

The logarithm transformation can be used

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

C

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the model that includes all six independent variablesshould be selected using the adjusted r² statistic.

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Question 3

Correct Answer:

Verified

False

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 developed a multiple regression model.The business literature involving human capital shows that education influences an individual's annual income.Combined,these may influence family size.With this in mind,what should the real estate builder be particularly concerned with when analysing the multiple regression model?

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Question 4

As a project for his business statistics class,a student examined the factors that determined parking metre rates throughout the campus area.Data were collected for the price per hour of parking,blocks to the quadrangle,and one of the three jurisdictions: on campus,in downtown and off campus,or outside of downtown and off campus.The population regression model hypothesised is Y_i = α + β₁x₁_i + β₂x₂_i + β₃x₃_i + ε_i Where Y is the metre price X₁ is the number of blocks to the quad X₂ is a dummy variable that takes the value 1 if the metre is located in downtown And off campus and the value 0 otherwise X₃ is a dummy variable that takes the value 1 if the metre is located outside of Downtown and off campus,and the value 0 otherwise Suppose that whether the metre is located on campus is an important explanatory factor.Why should the variable that depicts this attribute not be included in the model?

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Question 5

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. SUMMARY output Regression Statistics Multiple R 0.747 R Square 0.558 Adj. R Square 0.478 Std. Error 363.1 Observations 14 ANOVA df SS MS F Signưf F Regression 2 10344797 5172399 6.94 0.0110 Residual 11 8193929 744903 Total 13 18538726 Coeff StdErior Stat P -value Intercept 1283.0 352.0 3.65 0.0040 CenDose 25.228 3.631 2.92 0.0140 CenDoseSq 0.8604 0.3722 2.31 0.0410 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic curvilinear relationship between time and dose.The value of the test statistic is ________.

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Question 6

So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

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Question 7

If a person uses a multiple regression model when it is clear that model assumptions have not been met,this is a violation of ethics.

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Question 8

One transformation that may help overcome violations to the assumption of equal variance is the square-root transformation.

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Question 9

Instruction 16-2 A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model: Y = β₀ + β₁X + β₂X²+^ε where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: SUMMARY Regression Statistics Multiple R 0.994 R Square 0.988 Std. Error 12.42 Observations 12 ANOVA If SS MS F Sigưf F Regression 2 115145 57573 373 0.0001 Residual 9 1388 154 Total 11 116533 Coeff StdError Stat P -Value Intercept 286.42 9.66 29.64 0.0001 Price 0.31 0.06 -5.14 0.0006 Price Sq 0.000067 0.00007 0.95 0.3647 Note: Std.Error = Standard Error -Referring to Instruction 16-2,and noting that this model includes both a linear and a quadratic term,what is the correct interpretation of the coefficient of multiple determination?

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Question 10

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. SUMMARY output Regression Statistics Multiple R 0.747 R Square 0.558 Adj. R Square 0.478 Std. Error 363.1 Observations 14 ANOVA df SS MS F Signưf F Regression 2 10344797 5172399 6.94 0.0110 Residual 11 8193929 744903 Total 13 18538726 Coeff StdErior Stat P -value Intercept 1283.0 352.0 3.65 0.0040 CenDose 25.228 3.631 2.92 0.0140 CenDoseSq 0.8604 0.3722 2.31 0.0410 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a quadratic model without a linear term and a quadratic model that includes a linear term.The value of the test statistic is ________.

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Question 11

Instruction 16-1 To explain personal consumption (CONS)measured in dollars,data is collected for INC personal income in dollars \ 1 plus the credit limit in dollars available to the CRDTLIM individual average annualised percentage interest rate for APR: borrowing for the individual per person advertising expenditure in dollars by manufacturers in the city where the ADVT: individual lives GENDER: gender of the individual; 1 if female, 0 if male A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was = 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER -Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for ADVT?

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Question 12

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

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Question 13

Instruction 16-1 To explain personal consumption (CONS)measured in dollars,data is collected for INC personal income in dollars \ 1 plus the credit limit in dollars available to the CRDTLIM individual average annualised percentage interest rate for APR: borrowing for the individual per person advertising expenditure in dollars by manufacturers in the city where the ADVT: individual lives GENDER: gender of the individual; 1 if female, 0 if male A regression analysis was performed with CONS as the dependent variable and log(CRDTLIM),log(APR),log(ADVT),and GENDER as the independent variables.The estimated model was = 2.28 - 0.29 log(CRDTLIM)+ 5.77 log(APR)+ 2.35 log(ADVT)+ 0.39 GENDER -Referring to Instruction 16-1,and noting that ADVT has been transformed using the log transformation,what is the correct interpretation for the estimated coefficient for APR?

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Question 14

Instruction 16-2 A certain type of rare gem serves as a status symbol for many of its owners.In theory,for low prices,the demand decreases as the price of the gem increases.However,experts hypothesise that when the gem is valued at very high prices,the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus,the model proposed to best explain the demand for the gem by its price is the quadratic model: Y = β₀ + β₁X + β₂X²+^ε where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: SUMMARY output Regression Statistics Multiple R 0.994 R Square 0.988 Std. Error 12.42 Observations 12 ANOVA dff SS MS F Siguif F Regression 2 115145 57573 373 0.0001 Residual 9 1388 154 Total 11 116533 Coeff StdError t Stat P-Value Intercept 286.42 9.66 29.64 0.0001 Price -0.31 0.06 -5.14 0.0006 Price Sq p.000067 p.00007 p.95 p.3647 Note: Std.Error = Standard Error -Referring to Instruction 16-2,what is the value of the test statistic for testing whether the quadratic term is necessary in fitting in the response curve relating the demand (Y)and the price (X)?

(Multiple Choice)

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Question 15

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. SUMMARY output Regression Statistics Multiple R 0.747 R Square 0.558 Adj. R Square 0.478 Std. Error 363.1 Observations 14 ANOVA df SS MS F Signưf F Regression 2 10344797 5172399 6.94 0.0110 Residual 11 8193929 744903 Total 13 18538726 Coeff StdErior Stat P -value Intercept 1283.0 352.0 3.65 0.0040 CenDose 25.228 3.631 2.92 0.0140 CenDoseSq 0.8604 0.3722 2.31 0.0410 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use an F test to determine if there is a significant quadratic relationship between time and dose.The p-value of the test is ________.

(Short Answer)

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Question 16

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the model that includes X₁,X₅ and X₆should be among the appropriate models using the Mallow's C_p statistic.

(True/False)

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Question 17

Instruction 16-5 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a quadratic model to this data.The results obtained by Microsoft Excel follow. SUMMARY output Regression Statistics Multiple R 0.747 R Square 0.558 Adj. R Square 0.478 Std. Error 363.1 Observations 14 ANOVA df SS MS F Signưf F Regression 2 10344797 5172399 6.94 0.0110 Residual 11 8193929 744903 Total 13 18538726 Coeff StdErior Stat P -value Intercept 1283.0 352.0 3.65 0.0040 CenDose 25.228 3.631 2.92 0.0140 CenDoseSq 0.8604 0.3722 2.31 0.0410 Note: Adj.R Square = Adjusted R Square;Std.Error = Standard Error -Referring to Instruction 16-5,suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a quadratic model that includes a linear term.If she used a level of significance of 0.01,she would decide that the linear model is sufficient.

(True/False)

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Question 18

An independent variable X_j is considered highly correlated with the other independent variables if

(Multiple Choice)

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Question 19

Instruction 16-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker (X₁),the number of years of education received (X₂),the number of years at the previous job (X₃),a dummy variable for marital status (X₄: 1 = married,0 = otherwise),a dummy variable for head of household (X₅: 1 = yes,0 = no)and a dummy variable for management position (X₆: 1 = yes,0 = no). The coefficient of multiple determination (R²_j)the regression model using each of the 6 variables X_jas the dependent variable and all other X variables as independent variables are,respectively,0.2628,0.1240,0.2404,0.3510,0.3342 and 0.0993. The partial results from best-subset regression are given below: Model R Square Adj. R Square Std. Error X1X5Х6 0.4568 0.4116 18.3534 \times1\times2\times5\times6 0.4697 0.4091 18.3919 \times1\times3\times5\times6 0.4691 0.4084 18.4023 \times1\times2\times3\times5\times6 0.4877 0.4123 18.3416 \times1\times2\times3\times4\times5\times6 0.4949 0.4030 18.4861 -Referring to Instruction 16-6,the variable X₁ should be dropped to remove collinearity.

(True/False)

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Question 20

The logarithm transformation can be used

So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

If a person uses a multiple regression model when it is clear that model assumptions have not been met,this is a violation of ethics.

One transformation that may help overcome violations to the assumption of equal variance is the square-root transformation.

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

An independent variable X_j is considered highly correlated with the other independent variables if

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

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

Exam 16: Multiple Regression Model Building

The logarithm transformation can be used

So that we can fit curves as well as lines by regression,we often use mathematical manipulations for converting one variable into a different form.These manipulations are called dummy variables.

If a person uses a multiple regression model when it is clear that model assumptions have not been met,this is a violation of ethics.

One transformation that may help overcome violations to the assumption of equal variance is the square-root transformation.

One of the consequences of collinearity in multiple regression is inflated standard errors in some or all of the estimated slope coefficients.

An independent variable Xj is considered highly correlated with the other independent variables if

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

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

An independent variable X_j is considered highly correlated with the other independent variables if