outline solutions
OUTLINE SOLUTIONS
Regression Modelling (ST2210)
Internal test (30%)
12th November 2010
KNumber
Name
Course
Duration: 90 mins
Instructions:
Answer all questions in the spaces provided – (you may use backs of sheets and/or additional paper if required)
This is a CLOSED BOOK test. You can consult the test paper, KU tables and the attached output ONLY. You may use an approved calculator.
Use a 5% level of significance (α = 5%) where appropriate.
Fanfare International Inc. is a company that manufactures ceiling fans and lighting fixtures. These products are marketed and distributed to over 1000 lighting showrooms and electrical wholesalers by a team of 46 sales representatives.
Fanfare have decided they need to develop forecasts of future sales (y) to help determine future sales force needs. They investigated three factors that may affect sales, yearly advertising expenditure (adex) in thousands of pounds, number of housing starts (hsstart) in thousands of units and average mortgage rate (mtgrate) for 30 year loans (%). Data were collected for all 46 sales representatives.
The data is analysed in SAS using a multiple linear regression model, the variable names used in the SAS program appear in brackets above. Use the SAS output attached to answer the following questions.
(i) State the least squares estimate of the full regression model.
where x1 = advertising expenditure x2 = housing starts x3 = average mortgage rate
(2 marks)
continued…
(ii) Complete the ANOVA table for the full regression model below.
(6 marks)
Source df Sum of squares
Mean square
F value
Model
3
6681548
2227182.67
89.94
Error
42
1040082
24763.86
Total
45
7721630
(iii) Use an F test to test the global significance of the model, include your hypothesis, test statistics and your conclusion.
(4 marks)
H0 : β1 = β2 = β3 = 0
H1 : at least one of βi ≠ 0
F=89.94,
Regression Modelling (ST2210)
Internal test (30%)
12th November 2010
KNumber
Name
Course
Duration: 90 mins
Instructions:
Answer all questions in the spaces provided – (you may use backs of sheets and/or additional paper if required)
This is a CLOSED BOOK test. You can consult the test paper, KU tables and the attached output ONLY. You may use an approved calculator.
Use a 5% level of significance (α = 5%) where appropriate.
Fanfare International Inc. is a company that manufactures ceiling fans and lighting fixtures. These products are marketed and distributed to over 1000 lighting showrooms and electrical wholesalers by a team of 46 sales representatives.
Fanfare have decided they need to develop forecasts of future sales (y) to help determine future sales force needs. They investigated three factors that may affect sales, yearly advertising expenditure (adex) in thousands of pounds, number of housing starts (hsstart) in thousands of units and average mortgage rate (mtgrate) for 30 year loans (%). Data were collected for all 46 sales representatives.
The data is analysed in SAS using a multiple linear regression model, the variable names used in the SAS program appear in brackets above. Use the SAS output attached to answer the following questions.
(i) State the least squares estimate of the full regression model.
where x1 = advertising expenditure x2 = housing starts x3 = average mortgage rate
(2 marks)
continued…
(ii) Complete the ANOVA table for the full regression model below.
(6 marks)
Source df Sum of squares
Mean square
F value
Model
3
6681548
2227182.67
89.94
Error
42
1040082
24763.86
Total
45
7721630
(iii) Use an F test to test the global significance of the model, include your hypothesis, test statistics and your conclusion.
(4 marks)
H0 : β1 = β2 = β3 = 0
H1 : at least one of βi ≠ 0
F=89.94,