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# Anova and regression. Trend analysis

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49) If a quarterly seasonal index is 0.66, it implies that

A. the other three quarter percentages will total 34%
B. the quarter's sales are 6% above the yearly average
C. the quarter's sales are 66% of the year total sales
D. the quarter's sales are 66% of the yearly average

50) Given the trend equation Y' = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010?

A. 31
B. 25
C. 27
D. 32

51) The following linear trend equation was developed for the annual sales of the Tractor Manufacturing Company. Y' = 355 + 50t (in \$ thousands). How much are sales increasing by?

A. \$500,000 per year
B. \$5,000 per month
C. \$50,000 per year
D. \$6,000 per year

52) The owner of a local construction company that specializes in outdoor structures desires to make a prediction regarding the next business year sales. Expansion of the business is one possible decision that could be made. It has been determined that the business needs to be at least \$8 million dollars in annual sales before expansion could be considered. The following is data for the past 6 years. (Sales in millions of dollars.)

Year Sales Year Sales
2004 7.45 2007 7.94
2005 7.83 2008 7.76
2006 8.07 2009 7.90

The statistical analysis of the data produced this least square trend equation.

Y' = 7.634 + 0.05457t

What should the owner's decision be regarding expansion in 2010?

A. Expansion should be delayed
B. Expansion should be considered
C. Cannot make a decision based on this data
D. Expansion decision could go either way based on data

53) With the increased cost in fuel, there has been a shift in the buying habits of new car purchasers. A local car dealer was interested in determining if there was a significant difference in fuel efficiencies between three sizes of car: compact, midsize and large. The manager did a random sample of 27 cars. An ANOVA was used as the analysis tool using a significant level of .01. The results of the ANOVA were as follows:

Source of Variation SS df MS F p-value
Between Groups 130.44 2 65.22 7.97 0.0017
Within Groups 196.24 24 8.18
Total 326.68 36

The manager's decision would be

A. to reject the null hypothesis; there is a significant difference between cars
B. this was not the correct test for this data; a series of student t tests would have been better
C. to accept the null hypothesis; there is not a significant difference between cars
D. the mean fuel efficiency of the car cannot be compared

54) Big House Lumber Company, located in Dayton, Ohio, is preparing its annual business report. The manager has performed an analysis of the business annual sales starting in 2004 and concluding with 2009. This analysis produced an annual sales linear trend equation of Y' = 10.0989 + 0.14213t. The manager has been indicating to the company's investors that sales in 2011 will exceed \$11.5 million dollars. Is the manager statement accurate?

A. The manager is in need of more information before making a prediction.
B. The manager is overstating the annual sales.
C. The manager is providing the investors with a good prediction.
D. The manager has interpreted the data correctly.

https://brainmass.com/statistics/analysis-of-variance/anova-regression-trend-analysis-342125

#### Solution Preview

49) If a quarterly seasonal index is 0.66, it implies that

A. the other three quarter percentages will total 34%
B. the quarter's sales are 6% above the yearly average
C. the quarter's sales are 66% of the year total sales
D. the quarter's sales are 66% of the yearly average

Ans. C

50) Given the trend equation Y' = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010?

A. 31
B. 25
C. 27
D. 32

Ans. C

51) The following linear trend equation was developed for the annual sales of the Tractor Manufacturing Company. Y' = 355 + 50t (in \$ thousands). How much are sales increasing by?

A. \$500,000 per year
B. \$5,000 per month
C. \$50,000 per year
D. \$6,000 per year

Ans. C

52)
The owner of a local construction company that specializes in outdoor structures desires to make a prediction regarding the ...

#### Solution Summary

Finding components of a time series and also interpreting regression equation. For example
The following linear trend equation was developed for the annual sales of the Tractor Manufacturing Company. Y' = 355 + 50t (in \$ thousands). How much are sales increasing by?

A. \$500,000 per year
B. \$5,000 per month
C. \$50,000 per year
D. \$6,000 per year

\$2.49