See attached file for full problem description.

Suppose that the sales manager of a company wishes to evaluate the performance of the company's sales representatives. Each sales representative is solely responsible for one sales territory, and the manager decides that it is reasonable to measure performance of a sales representative by using the yearly sales of the company's product in the representative's sales territory (Y). The manager feels that the sales performance depends on the following five independent variables:

X1 = number of months the representative has been employed by the company

X2 = sales of the company's product and competing products in the sales territory

X3 = dollar advertising expenditure in the territory

X4 = weighted average if the company's market share in the territory for the previous four years

X5 = change in the company's market share in the territory over the previous four years

a) Please write down the regression equation between Y as the dependent variable and X1,X2,X3,X4 and X5 as independent variables.

b) Please interpret all regression coefficients in the context of the above problem (i.e. β0, β1, ,β5).

c) Determine the standard error of the estimate, coefficient of determination and the adjusted coefficient of determination.

d) At the 0.01 level of significance, which of the independent variables have significant effects?

e) Using a 0.01 level of significance, do you think that at least one of the independent variables provide any explanatory power in predicting Y?

Please state your hypothesis clearly (both verbally and symbolically). Also briefly explain the testing procedure (namely what type of test you are using and why you are using it).

f) Calculate the VIFs for the variables X1 and X2.

g) Do you think there exists multi-colinearity in the model? Why or why not?

h-i-j) Please check the validity of your model, in other words check whether the

regression assumptions (all three of them) hold in your model. In doing so, please briefly

explain your reasoning (state your hypothesis', test statistics, rejection regions and

conclusions for all 3).

Please use the following JMP-IN output to in order to answer the above questions.

For the regression between Y and X1, ,X5

Summary of Fit

RSquare ?

RSquare Adj 0.892643

Root Mean Square Error ?

Mean of Response 3374.568

Observations (or Sum Wgts) 25

Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model 5 37862659 7572532 ?

Error 19 3516890 185099 Prob > F

C. Total 24 41379549 ?

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -1113.788 419.8869 ? ?

TimewithCompany, X1 3.6121012 1.1817 ? ?

MarketPot, X2 0.0420881 0.006731 ? ?

Advertising, X3 0.1288568 0.037036 ? ?

Market Share, X4 256.95554 39.13607 ? ?

MarketShareChange, X5 324.53345 157.2831 ? ?

Durbin-Watson

Durbin-Watson Number of Obs. AutoCorrelation

1.761867 25 0.1014

The distribution of the residuals from the regression of Y vs. X1, ,X5

Goodness-of-Fit Test

Shapiro-Wilk W Test

W Prob0.944057 0.1836

For the regression between the squared residuals and X1, , X5

Summary of Fit

RSquare 0.235809

RSquare Adj 0.034707

Root Mean Square Error 165894.6

Mean of Response 140675.6

Observations (or Sum Wgts) 25

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -205532 161905.7 -1.27 0.2196

TimewithCompany -249.9095 455.6559 -0.55 0.5898

MarketPot 4.3155604 2.595516 1.66 0.1128

Advertising 9.7092021 14.28088 0.68 0.5048

Market Share 22038.486 15090.62 1.46 0.1605

MarketShareChange -90037.44 60647.34 -1.48 0.1541

For the regression between X1 and X2, ,X5

Summary of Fit

RSquare 0.266888

RSquare Adj 0.120265

Root Mean Square Error 81.41049

Mean of Response 87.642

Observations (or Sum Wgts) 25

For the regression between X2 and X1,X3,X4,X5

Summary of Fit

RSquare 0.310709

RSquare Adj 0.172851

Root Mean Square Error 14292.02

Mean of Response 38858.05

Observations (or Sum Wgts) 25

Correlations between Y,X1, ,X5

Sales TimewithCompany MarketPot Advertising Market Share MarketShareChange

Sales 1.0000 0.6229 0.5978 0.5962 0.4835 0.4892

TimewithCompany 0.6229 1.0000 0.4540 0.2492 0.1062 0.2515

MarketPot 0.5978 0.4540 1.0000 0.1741 -0.2107 0.2683

Advertising 0.5962 0.2492 0.1741 1.0000 0.2645 0.3765

Market Share 0.4835 0.1062 -0.2107 0.2645 1.0000 0.0855

MarketShareChange 0.4892 0.2515 0.2683 0.3765 0.0855 1.0000

Suppose that the sales manager of a company wishes to evaluate the

performance of the companyâs sales representatives. Each sales

representative is solely responsible for one sales territory, and the

manager decides that it is reasonable to measure performance of a sales

representative by using the yearly sales of the companyâs product in

the representativeâs sales territory (Y). The manager feels that the

sales performance depends on the following five independent variables:

X1 = number of months the representative has been employed by the

company

X2 = sales of the companyâs product and competing products in the

sales territory

X3 = dollar advertising expenditure in the territory

X4 = weighted average if the companyâs market share in the territory

for the previous four years

X5 = change in the companyâs market share in the territory over the

previous four years

a) Please write down the regression equation between Y as the dependent

variable and X1,X2,X3,X4 and X5 as independent variables.

b) Please interpret all regression coefficients in the context of the

above problem (i.e. Î²0, Î²1, â¦ ,Î²5).

c) Determine the standard error of the estimate, coefficient of

determination and the adjusted coefficient of determination.

d) At the 0.01 level of significance, which of the independent variables

have significant effects?

e) Using a 0.01 level of significance, do you think that at least one of

the independent variables provide any explanatory power in predicting Y?

Please state your hypothesis clearly (both verbally and symbolically).

Also briefly explain the testing procedure (namely what type of test you

are using and why you are using it).

f) Calculate the VIFs for the variables X1 and X2.

g) Do you think there exists multi-colinearity in the model? Why or why

not?

h-i-j) Please check the validity of your model, in other words check

whether the

regression assumptions (all three of them) hold in your model. In doing

so, please briefly

explain your reasoning (state your hypothesisâ, test statistics,

rejection regions and

conclusions for all 3).

Please use the following JMP-IN output to in order to answer the above

questions.

For the regression between Y and X1,â¦,X5

Summary of Fit

RSquare ?

RSquare Adj 0.892643

Root Mean Square Error ?

Mean of Response 3374.568

Observations (or Sum Wgts) 25

Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model 5 37862659 7572532 ?

Error 19 3516890 185099 Prob > F

C. Total 24 41379549 ?

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -1113.788 419.8869 ? ?

TimewithCompany, X1 3.6121012 1.1817 ? ?

MarketPot, X2 0.0420881 0.006731 ? ?

Advertising, X3 0.1288568 0.037036 ? ?

Market Share, X4 256.95554 39.13607 ? ?

MarketShareChange, X5 324.53345 157.2831 ? ?

Durbin-Watson

Durbin-Watson Number of Obs. AutoCorrelation

1.761867 25 0.1014

The distribution of the residuals from the regression of Y vs. X1,â¦,X5

Goodness-of-Fit Test

Shapiro-Wilk W Test

W Prob

0.944057 0.1836

For the regression between the squared residuals and X1, â¦, X5

Summary of Fit

RSquare 0.235809

RSquare Adj 0.034707

Root Mean Square Error 165894.6

Mean of Response 140675.6

Observations (or Sum Wgts) 25

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -205532 161905.7 -1.27 0.2196

TimewithCompany -249.9095 455.6559 -0.55 0.5898

MarketPot 4.3155604 2.595516 1.66 0.1128

Advertising 9.7092021 14.28088 0.68 0.5048

Market Share 22038.486 15090.62 1.46 0.1605

MarketShareChange -90037.44 60647.34 -1.48 0.1541

For the regression between X1 and X2,â¦,X5

Summary of Fit

RSquare 0.266888

RSquare Adj 0.120265

Root Mean Square Error 81.41049

Mean of Response 87.642

Observations (or Sum Wgts) 25

For the regression between X2 and X1,X3,X4,X5

Summary of Fit

RSquare 0.310709

RSquare Adj 0.172851

Root Mean Square Error 14292.02

Mean of Response 38858.05

Observations (or Sum Wgts) 25

Correlations between Y,X1,â¦,X5

r

s

Ñ

Ñ

Ð

Ð

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

æÈ¤Âæ¬â¤

æ§ä²ÃÂæ¬ì¤

Ð A

Ð A

pæ¬é¤

Ð¢

Ð¢

Ð¢

Ð¢

Ò

Ò

Ò

Ò

Ò

Ò

Ò

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

0.1741 1.0000 0.2645 0.3765

Market Share 0.4835 0.1062 -0.2107 0.2645 1.0000 0.0855

MarketShareChange 0.4892 0.2515 0.2683 0.3765 0.0855 1.0000

Suppose that the sales manager of a company wishes to evaluate the performance of the company's sales representatives. Each sales representative is solely responsible for one sales territory, and the manager decides that it is reasonable to measure performance of a sales representative by using the yearly sales of the company's product in the representative's sales territory (Y). The manager feels that the sales performance depends on the following five independent variables:

X1 = number of months the representative has been employed by the company

X2 = sales of the company's product and competing products in the sales territory

X3 = dollar advertising expenditure in the territory

X4 = weighted average if the company's market share in the territory for the previous four years

X5 = change in the company's market share in the territory over the previous four years

a) Please write down the regression equation between Y as the dependent variable and X1,X2,X3,X4 and X5 as independent variables.

b) Please interpret all regression coefficients in the context of the above problem (i.e. β0, β1, ,β5).

c) Determine the standard error of the estimate, coefficient of determination and the adjusted coefficient of determination.

d) At the 0.01 level of significance, which of the independent variables have significant effects?

e) Using a 0.01 level of significance, do you think that at least one of the independent variables provide any explanatory power in predicting Y?

Please state your hypothesis clearly (both verbally and symbolically). Also briefly explain the testing procedure (namely what type of test you are using and why you are using it).

f) Calculate the VIFs for the variables X1 and X2.

g) Do you think there exists multi-colinearity in the model? Why or why not?

h-i-j) Please check the validity of your model, in other words check whether the

regression assumptions (all three of them) hold in your model. In doing so, please briefly

explain your reasoning (state your hypothesis', test statistics, rejection regions and

conclusions for all 3).

Please use the following JMP-IN output to in order to answer the above questions.

For the regression between Y and X1, ,X5

Summary of Fit

RSquare ?

RSquare Adj 0.892643

Root Mean Square Error ?

Mean of Response 3374.568

Observations (or Sum Wgts) 25

Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model 5 37862659 7572532 ?

Error 19 3516890 185099 Prob > F

C. Total 24 41379549 ?

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -1113.788 419.8869 ? ?

TimewithCompany, X1 3.6121012 1.1817 ? ?

MarketPot, X2 0.0420881 0.006731 ? ?

Advertising, X3 0.1288568 0.037036 ? ?

Market Share, X4 256.95554 39.13607 ? ?

MarketShareChange, X5 324.53345 157.2831 ? ?

Durbin-Watson

Durbin-Watson Number of Obs. AutoCorrelation

1.761867 25 0.1014

The distribution of the residuals from the regression of Y vs. X1, ,X5

Goodness-of-Fit Test

Shapiro-Wilk W Test

W Prob0.944057 0.1836

For the regression between the squared residuals and X1, , X5

Summary of Fit

RSquare 0.235809

RSquare Adj 0.034707

Root Mean Square Error 165894.6

Mean of Response 140675.6

Observations (or Sum Wgts) 25

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -205532 161905.7 -1.27 0.2196

TimewithCompany -249.9095 455.6559 -0.55 0.5898

MarketPot 4.3155604 2.595516 1.66 0.1128

Advertising 9.7092021 14.28088 0.68 0.5048

Market Share 22038.486 15090.62 1.46 0.1605

MarketShareChange -90037.44 60647.34 -1.48 0.1541

For the regression between X1 and X2, ,X5

Summary of Fit

RSquare 0.266888

RSquare Adj 0.120265

Root Mean Square Error 81.41049

Mean of Response 87.642

Observations (or Sum Wgts) 25

For the regression between X2 and X1,X3,X4,X5

Summary of Fit

RSquare 0.310709

RSquare Adj 0.172851

Root Mean Square Error 14292.02

Mean of Response 38858.05

Observations (or Sum Wgts) 25

Correlations between Y,X1, ,X5

Sales TimewithCompany MarketPot Advertising Market Share MarketShareChange

Sales 1.0000 0.6229 0.5978 0.5962 0.4835 0.4892

TimewithCompany 0.6229 1.0000 0.4540 0.2492 0.1062 0.2515

MarketPot 0.5978 0.4540 1.0000 0.1741 -0.2107 0.2683

Advertising 0.5962 0.2492 0.1741 1.0000 0.2645 0.3765

Market Share 0.4835 0.1062 -0.2107 0.2645 1.0000 0.0855

MarketShareChange 0.4892 0.2515 0.2683 0.3765 0.0855 1.0000

Suppose that the sales manager of a company wishes to evaluate the

performance of the companyâs sales representatives. Each sales

representative is solely responsible for one sales territory, and the

manager decides that it is reasonable to measure performance of a sales

representative by using the yearly sales of the companyâs product in

the representativeâs sales territory (Y). The manager feels that the

sales performance depends on the following five independent variables:

X1 = number of months the representative has been employed by the

company

X2 = sales of the companyâs product and competing products in the

sales territory

X3 = dollar advertising expenditure in the territory

X4 = weighted average if the companyâs market share in the territory

for the previous four years

X5 = change in the companyâs market share in the territory over the

previous four years

a) Please write down the regression equation between Y as the dependent

variable and X1,X2,X3,X4 and X5 as independent variables.

b) Please interpret all regression coefficients in the context of the

above problem (i.e. Î²0, Î²1, â¦ ,Î²5).

c) Determine the standard error of the estimate, coefficient of

determination and the adjusted coefficient of determination.

d) At the 0.01 level of significance, which of the independent variables

have significant effects?

e) Using a 0.01 level of significance, do you think that at least one of

the independent variables provide any explanatory power in predicting Y?

Please state your hypothesis clearly (both verbally and symbolically).

Also briefly explain the testing procedure (namely what type of test you

are using and why you are using it).

f) Calculate the VIFs for the variables X1 and X2.

g) Do you think there exists multi-colinearity in the model? Why or why

not?

h-i-j) Please check the validity of your model, in other words check

whether the

regression assumptions (all three of them) hold in your model. In doing

so, please briefly

explain your reasoning (state your hypothesisâ, test statistics,

rejection regions and

conclusions for all 3).

Please use the following JMP-IN output to in order to answer the above

questions.

For the regression between Y and X1,â¦,X5

Summary of Fit

RSquare ?

RSquare Adj 0.892643

Root Mean Square Error ?

Mean of Response 3374.568

Observations (or Sum Wgts) 25

Analysis of Variance

Source DF Sum of Squares Mean Square F Ratio

Model 5 37862659 7572532 ?

Error 19 3516890 185099 Prob > F

C. Total 24 41379549 ?

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -1113.788 419.8869 ? ?

TimewithCompany, X1 3.6121012 1.1817 ? ?

MarketPot, X2 0.0420881 0.006731 ? ?

Advertising, X3 0.1288568 0.037036 ? ?

Market Share, X4 256.95554 39.13607 ? ?

MarketShareChange, X5 324.53345 157.2831 ? ?

Durbin-Watson

Durbin-Watson Number of Obs. AutoCorrelation

1.761867 25 0.1014

The distribution of the residuals from the regression of Y vs. X1,â¦,X5

Goodness-of-Fit Test

Shapiro-Wilk W Test

W Prob

0.944057 0.1836

For the regression between the squared residuals and X1, â¦, X5

Summary of Fit

RSquare 0.235809

RSquare Adj 0.034707

Root Mean Square Error 165894.6

Mean of Response 140675.6

Observations (or Sum Wgts) 25

Parameter Estimates

Term Estimate Std Error t Ratio Prob>|t|

Intercept -205532 161905.7 -1.27 0.2196

TimewithCompany -249.9095 455.6559 -0.55 0.5898

MarketPot 4.3155604 2.595516 1.66 0.1128

Advertising 9.7092021 14.28088 0.68 0.5048

Market Share 22038.486 15090.62 1.46 0.1605

MarketShareChange -90037.44 60647.34 -1.48 0.1541

For the regression between X1 and X2,â¦,X5

Summary of Fit

RSquare 0.266888

RSquare Adj 0.120265

Root Mean Square Error 81.41049

Mean of Response 87.642

Observations (or Sum Wgts) 25

For the regression between X2 and X1,X3,X4,X5

Summary of Fit

RSquare 0.310709

RSquare Adj 0.172851

Root Mean Square Error 14292.02

Mean of Response 38858.05

Observations (or Sum Wgts) 25

Correlations between Y,X1,â¦,X5

r

s

Ñ

Ñ

Ð

Ð

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

æÈ¤Âæ¬â¤

æ§ä²ÃÂæ¬ì¤

Ð A

Ð A

pæ¬é¤

Ð¢

Ð¢

Ð¢

Ð¢

Ò

Ò

Ò

Ò

Ò

Ò

Ò

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

Ð¢

0.1741 1.0000 0.2645 0.3765

Market Share 0.4835 0.1062 -0.2107 0.2645 1.0000 0.0855

MarketShareChange 0.4892 0.2515 0.2683 0.3765 0.0855 1.0000

### Recently Asked Questions

- Construct a sound chain argument with the following conclusion: "If you're in Texas, you're in the U.S."

- (For 1970s-1980) Aggregate expenditure is the total amount of spending in the economy that determines the level of the GDP. Components of aggregate expenditure

- Please help me with this problem!! I would like to know the process by which you obtain the answer, not just the answer. Thank you.