Reference no: EM132402844

Assignment -

The following problem information is to be used for problems 5 through 11.

Suppose that a company was trying to relate the number of units ordered to the offered price of the product. The computer printout provided the following equation:

Number of Units = 1000 - 20 Price

Additionally, the printout gave the following information about the Price coefficient, the R-square value and the Standad Error of the Regression.

PREDICTOR COEF. SE COEF. T P

Price - 20 2 2.04 ,015

s = 50 R-Sq = 80

5. What percent of the variation in NUMBER OF UNITS can be associated with the PRICE being offered?

A. 20

b. 80

6. What is the nature of the relationship (note the sign of the slope)?

A. Positive

b. Negative

7. If the price were to increase $1, what would be the anticipated change in Number of Units Ordered?

A. - 20

b. 86.32

8. Given the generic model of y = β0 + β1x, the null hypothesis would be

A. Ho: β0 = 0

b. Ho: β1 = 0

9. Given the p value of .015, what would be the conclusion to the test?

A. Accept Ha: I am at least 95% sure that β1 = 0

b. Accept Ha: I am at least 95% sure that β1 ≠ 0

c. Accept Ho: I am at least 95% sure that β0 = 1000

10. What would be the predicted number of units order if the price was $20/unit?

A. 400

b. 600

11. What would be a 95% confidence interval of sales (use Z = 2) if the price was $20/unit (Note: The precision will now be ± 2 standard deviations)?

A. 200 to 600

b. 500 to 700

12. This introduction applies to Problems 12 and 13.

A simple linear relationship between the price and size of a home has ALREADY been found to be statistically significant. Since the amount of variation is still too large to make a practical confidence interval, the variable factor "type of home construction" (a nominal variable) is to be introduced into the model. Five types of home construction are of interest: brick, vinyl, stone, wood and steel.

How many additional "factors" are to be introduced into the multivariate equation?

A. 1

b. 10

13. How many levels of the factor "type of home construction" (that is, how many dummy variables) will be introduced into the equation?

A. 1

b. 4

14. Given that the computer of the relationship is as follows:

MODEL: PRICE = 35.40*SIZE +11000 BRICK +3500 VINYL + 3000 STONE + 6000 WOOD + 22500

Note: Since STEEL is not in the equation, it is the basis variable.

What is the average premium that one has to pay to have a brick home over a steel home?

A. $35.40

b. $11,000

15. For problem 14, what is the average premium that one has to pay to have a brick home rather than a vinyl home (Note the difference in coefficients in the brick and vinyl homes)?

A. $11,000

b. $7500

16. For problem 14, what would be the predicted price of a BRICK home of 2000 square feet?

A. $104.300

b. $93,300

This introduction applies to problems 17, 18, and 19.

James Gleason tried to say that he was selling older homes than the other agencies. SUPPOSE an appropriate statistical analysis was performed resulting in a

P value = .02.

17. What would be the appropriate statistical analysis tool that would have been used?

A. Simple linear regression

b. Analysis of Variance

c. Crosstabs

18. A positive regression line has a line that is sloping upward on a graph of y vs. x

True

False

19. The coefficient of determination represents the percent of variation in y related to variation in x.

True

False

30. As the value of r approaches 0, then the scatter graph shows no pattern.

True

False

31. Given the equation of y = 2 + 6 x, value of y if x is 3 is 18.

True

False

32. In count data tests, large values of Chi Square imply that there is little deviation between observed cell frequencies and expected cell frequencies.

True

False

33. Qualitative variables (nominal or ordinal) can be introduced into regression models and are know as factors.

True

False

34. The intensity of a qualitative variable in a multivariate equation is known as a level.

True

False

35. If a multivariate model has two independent variables (one quantitative and one qualitative) that are significant, the model will be represented by a series of multiple parallel lines.

True

False

36. The multiple coefficient of determination represents the amount of variation in y that will be explained by the total variation in all independent variables.

True

False

37. At test on an individual coefficient that has a corresponding p value of less than 5% would indicate that a particular coefficient is significant.

True

False

38. For the remaining problems on the test, open the file Metrtst.mtw from Blackboard/Mgt. 320/Course documents/Course Data Files/Test Files (noted as Metro Realty pop Test File #2).

Codes for the file are: Month: March = 3, April = 4, May = 5, June = 6 : Area: Dallas = 1, Ft. Worth = 2, Outlying Area = 3 ; Agency: 0 = Other, 1 = Metro

What percent of the homes in the metropolitan area were sold in the Dallas area?

A. 52.56%

b. 47.37%

39. What was the average selling price of all homes sold in the Metroplex (all cases)?

A. $92,455

b. $93,240

40. What was the sample standard deviation of all homes sold in the Metroplex (all cases)?

A. $18,155

b. $19,224

41. What is the average selling prices of the homes in Dallas only?

A. $93,240

b. $104,068

42. The newspaper article that precipitated the two complaining home sellers indicated that the average selling price of the homes for the past 12 months in the metropolitan area had been $104, 250 (remember to go back to the original worksheet of all cases). Since the actual average selling prices were much lower, which of the following describes how the timing of the gathering of data could affect the results.

A. The prices of the homes over the past 12 months had been relatively stable.

b. The prices of the homes over the past 12 months had been falling.

43. The following question also encompasses problems 43 - 45.

The validity of the newspaper article that stated that the average selling prices of homes in the Metro area (all cases) was $104,250 was being questioned. Answer the following questions about the newspaper article.

A. Ha: The average selling price of the homes is 104,250

b. Ha: The average selling price of the homes is different from 104,250

44. The t value and p-value for the hypothesis test is:

A. t = -10.82 and p = .000

b. t = -12.40 and p = .000

45. The conclusion to the test is that:

A. Accept Ho: I am at least 95% sure that the average prices are different from 104,250.

b. Accept Ha: I am at least 95% sure that the average prices are different from 104,250.

46. One of the individuals complaining about his selling price sold his home for $88,500. What would be the equivalent percentile ranking of that home relative to the selling prices of all homes in the Metroplex?

A. 42.8%

b. 39.7%

47. The coefficient of correlation between the size of the home and the number of bedrooms is:

A. .659

b. 2.87

48. If the value of the coefficient of correlation between the size of a home and the number of bedrooms had been 0.78, which of the following options would relate to that value?

A. Bigger homes have more bedrooms

b. More bedrooms means that the price of the home will increase.

49. The following information related to problems 49 - 51.

The statistical analyst decided to develop a simple linear equation that would relate the price of a home with the size of the home with Price being the dependent variable.

What is the least squares equation (best fit equation and/or regression equation) that describes the relationship?

A. Price = 22, 359 + 39.21 Size

b. Price = 21,369 + 38.6 Size

50. Based on the correct equation, what would be the incremental price per square foot of a home in the Metroplex?

A. $38.6/sq.ft.

b. $22,359

51. What percent of variation in price could be associated with the variation in the size of the home?

A. 52.7%

b. 50.2%

52. This information applies to problems 52-56.

The analyst is also interested in determining if some of the nominal variables can be significantly related to the " key variable" price. First of all, the analyst desires to know if there are statistically significant differences in the mean prices of homes between the three areas (Dallas, Ft. Worth, and the Outlying Areas).

The null hypothesis would be:

A. At least one average home price in one of the areas is different from the others

b. The average home prices in all three areas is equal.

53. The appropriate statistical tool to be chosen would be:

A. Regression

b. Analysis of Variance

c. Crosstabs

54. The F value and p value for the appropriate test is:

A. F = 98.46 and p = .000

b. F = 21.6 and p = .224

55. Based on the analysis, what is the average home prices in Dallas?

a. $104,068

b. $95,281

56. What Tukey values would establish if the average price of homes in Dallas is statistically and repeatably greater than the prices of homes in Ft. Worth?

A. -6392 to 3344

b. -23898 to - 16086

57. The information below relates to problems 57 - 61.

Was Metro selling far more homes proportionally in the lower priced areas of the metropolitan area (that is, Ft Worth and the Outlying areas) than the other agencies.

The alternate hypothesis to the test would be:

A. Ha: The average price is different for the different agencies.

b. Ha: Each agency sells a proportionate number of homes in each area.

c. Ha: Each agency does not sell a proportionate number of homes in each area.

58. What is the Chi Sq. and p value that would be associated with the appropriate statistical test for the problem?

a. Chi Square = 18.46 and p = 0148

b. Chi Square = 22.758 and p = .000

c. Chi Square = 8.32 and p = .322

59. Exactly how many of the homes that are sold by Metro Agency are sold in the Dallas area?

a. 4

b. 6

60. What percent of the homes that are sold by Metro are located in the Dallas area?

a. 12.42%

b. 10.53%

61. If Metro Agency had been selling its proportional share of homes in each area, how many homes would Metro have sold in the Dallas area?

a. 18

b. 20

62. The following information relates to problems 62 - 66.

The analyst decided to formulate an examine the following equation : Price = f(Size and Area).

What is the multivariate equation that predicts price as a function of the size and area?

a. Price = 40509+ 40.75 Size -13381 Area

b. Price = 5277+ 40 Size + 24,669 Area (1) + 5403 Area (2)

63. What percent of the variation in price is associated with the size AND the area of the house?

a. 88.2%

b. 85.2%

64. What is the indicated incremental price per square foot of a home in the appropriate model?

a. 40.75

b. 40.00

65. What is the expected average price differential between a home in Dallas and a home in the Outlying area?

a. $13,381

b. $24,669

66. What would be the predicted price of a home that was 1700 sq. ft. and that was located in the Outlying Area?

a. $75,256

b. none of the above.

Attachment:- Assignment Files.rar