1. A company that produces wood stains can purchase a particular additive from four different suppliers: Supplier A, B, C, or D. Eight different samples were selected from each supplier and the resulting color measurement (Color) was recorded for each sample. The data can be found in the file txt (variable names in first row).
2. Confirm the following regression model

Color = 41.95 – 0.30125 A – 0.6675 B + 0.5425 C is correct by

• Creating indicator variables in a SAS data step appropriate for representing the categorical variable Supplier in a regression model (original data given in the file txt which will first need to be placed in data lines to be read by a SAS data step).
• Fit the regression model using the indicator variables and provide output that shows parameter estimates.

1. Refer to the parameter estimates table in 1(a). Explain what each coefficient tells us about the different suppliers.
2. Based on the regression analysis in 1(a), interpret the individual t-tests for the coefficients of the indicator variables. Make sure to provide the appropriate output table.
3. Based on the regression analysis in 1(a), interpret the value of R². Make sure to provide the appropriate output table.
4. Based on the regression analysis in 1(a), interpret ANOVA table (from PROC REG). Make sure to provide the appropriate output table.

 

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2. A popular fast-food restaurant wanted to compare drive-through traffic for six days of the week (closed on Sundays): Mon, Tue, Wed, Thu, Fri, and Sat. Observations were made over 7 randomly selected time periods from each day (6 x 7 = 42 observation were made for the entire study).
   1. Complete the following ANOVA table quantities by hand. (You do not have to use SAS for this part but include the completed table in your output document.)

Source

DF

SS

MS

F

Day                                                                3855

Error

Total                                                              7887

 

1. What does the MS for Day tell you?
2. Use SAS to determine the p-value for the above table. This can be accomplished by using the =cdf(‘F’,F,df1,df2) function in a SAS data step (remember that the cdf function gives left-tail probabilities and the p-value is a right-tail probability).
3. Describe the hypotheses tested by the F-test in the table and, using the p-value from part (c), give the appropriate conclusion.

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3. A SAS data step is provided in the file txt and may be copied into SAS Studio to produce the data set. The data consists of colony forming units (Cfu) measured in an organic ingredient for a probiotic supplement. The classification levels were the four different seasons of the year (fall, winter, spring, and summer) and serve as the treatment groups.  The Cfu activity was believed to be seasonal in the ingredient. Several samples from each season were collected and each sample’s Cfu activity was determined (measured in millions of units).
   1. Why should we not use two-sample t-tests to see what differences there are between the means of these treatment groups?
   2. Produce an ANOVA table to test for differences between the seasons. What do you conclude? Explain.
   3. Produce Tukey’s HSD test to find any differences that exists between the treatment groups. Comment on your findings.

 

4. Two fragrances of air fresheners were used in eight different vehicles. The number of days that the fragrance was detectable was recorded.  Once one air freshener’s odor was undetectable in a vehicle, it was replaced by the other type of air freshener.  The data is provided in the file txt (variable names in the first row) and shown in the table below:

Fragrance/Car	1	2	3	4	5	6	7	8
Lavender	92	126	114	106	89	121	109	104
Lemon	88	105	97	101	89	108	83	106

 

1. Find the mean days lasted for the entire data set and then for each type of air freshener to estimate the effects (α1 and α2) for each type. You may use Proc Means in SAS to calculate the necessary means. From those means, the effects may be derived by hand.
2. Provide the ANOVA table for the two-way model for this randomized block design. Does the type of air freshener appear to make a difference in the days lasted? Explain.
3. It was noted that the experiment might have been conducted inconsistently between cars as some drivers may have replaced the air freshener right away while others may have waited a few days. It was thought this could lead to some cross-contamination.  Does the car appear to make a difference in the days the air fresheners lasted? Explain.

 

5. Three types of grass seed mixes (winter mix, spring mix, and a control) were planted in various plots over two different years. The response variable was Biomass, a measure of how much grass growth there was. The SAS data step that produces the resulting data set is contained in the file txt and can be copied, pasted into SAS Studio, and run to create the data set. The experiment can be analyzed using a two-way ANOVA with replication.
   1. Produce the ANOVA table including the model breakdown table. Which effect(s) appear to be significant?
   2. Run Tukey’s HSD test on the variable Mix. What can you say about the differences between the grass seed mixes?
   3. Provide the interaction plot between Mix and Year. Does the plot support your evaluation of the significance of the interaction effect? Explain.

 

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