Develop a linear trend expression

Assignment Help Applied Statistics

Reference no: EM131800001

Assignment Questions -

Q1. Part of an ANOVA table is shown below.

Source of Variation	Sum of Squares	Degree of Freedom	Mean Square	F
Between treatments	90	3	?	?
Within treatments (Error)	120	20	?
Total	?	?

a. Compute the missing values and fill in the blanks in the above table. Use α = .01 to determine if there is any significant difference among the means.

b. How many groups have there been in this problem?

c. What has been the total number of observations?

Q2. The sales records of a major auto manufacturer over the past 10 years are shown below.

Year (t)	Number of Cars Sold (in 1000s of Units)
1	195
2	200
3	250
4	270
5	320
6	380
7	440
8	460
9	500
10	500

Develop a linear trend expression and project the sales (the number of cars sold) for time period t = 11.

Q3. The following data represent the number of flash drives sold per day at a local computer shop and their prices.

Price (x)	Units Sold (y)
$34	3
36	4
32	6
35	5
30	9
38	2
40	1

a. Perform an F test and determine if the price and the number of flash drives sold are related. Let α = .01.

b. Perform a t test and determine if the price and the number of flash drives sold are related. Let α = .01.

Q4. In a completely randomized experimental design, 14 experimental units were used for each of the five levels of the factor (i.e., five treatments). Fill in the blanks in the following ANOVA table.

Source of Variation	Sum of Squares	Degree of Freedom	Mean Square	F
Between treatments	?	?	800.00	?
Within treatments (Error)	?	?	?
Total	10,600	?

Q5. Halls, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (In $1,000s) are shown below.

Store 1	Store 2	Store 3
46	34	33
47	36	31
45	35	35
42	39
45

At a 5% level of significance, test to see if there is a significant difference in the average sales of the three stores.

Q6. The marketing department of a company has designed three different boxes for its product. It wants to determine which box will produce the largest amount of sales. Each box will be test marketed in five different stores for a period of a month. Below is the information on sales.

	Store 1	Store 2	Store 3	Store 4	Store 5
Box 1	210	230	190	180	190
Box 2	195	170	200	190	193
Box 3	295	275	290	275	265

a. State the null and alternative hypotheses.

b. Construct an ANOVA table.

c. What conclusion do you draw?

Q7. Three different brands of tires were compared for wear characteristics. For each brand of tire, 10 tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below.

	Brand A	Brand B	Brand C
Average mileage	37	38	33
Sample variance	3	4	2

Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let α = .05

Q8. John has collected the following information on the amount of tips he received from parking cars the last seven nights.

Day	Tips
1	18
2	22
3	17
4	18
5	28
6	20
7	12

a. Compute the three-day moving averages for the time series.

b. Compute the mean square error for the forecasts.

c. Compute the mean absolute deviation for the forecasts.

Q9. The Very Fresh Juice Company has developed a regression model relating sales (y in $10,000s) with four independent variables. The four independent variables are price per unit (x1, in dollars), competitor's price (x2, in dollars), advertising (x3, in $1000s), and type of container used (x4) (1 = Cans and 0 = Bottles). Part of the regression results is shown below.

Source of Variation	Degree of Freedom	Sum of Squares	Mean Square	F
Regression	4	283,940.60
Error	18	621,735.14
Total

a. Compute the coefficient of determination and fully interpret its meaning.

b. Is the regression model significant? Explain what your answer implies. Let α = .05.

c. What has been the sample size for this analysis?

Q10. The prices of Rawlston, Inc. stock (y) over a period of 12 days, the number of shares (in 100s) of the company's stocks sold (x1), and the volume of exchange (in millions) on the New York Stock Exchange (x2) are shown below.

Day	(y)	(x1)	(x2)
1	87.50	950	11.00
2	86.00	945	11.25
3	84.00	940	11.75
4	83.00	930	11.75
5	84.50	935	12.00
6	84.00	935	13.00
7	82.00	932	13.25
8	80.00	938	14.50
9	78.50	925	15.00
10	79.00	900	16.50
11	77.00	875	17.00
12	77.50	870	17.50

Excel was used to determine the least squares regression equation. Part of the computer output is shown below.

ANOVA

	df	SS	MS	F	Significance F
Regression	2	118.8474	59.4237	40.9216	0.0000
Residual	9	13.0692	1.4521
Total	11	131.9167

	Coefficients	Standard Error	t Stat	P-value
Intercept	118.5059	33.5753	3.5296	0.0064
(x₁)	-0.0163	0.0315	-0.5171	0.6176
(x₂)	-1.5726	0.3590	-4.3807	0.0018

a. Use the output shown above and write an equation that can be used to predict the price of the stock.

b. Interpret the coefficients of the estimated regression equation that you found in part (a).

c. At 95% confidence, determine which variables are significant and which are not.

d. If on a given day, the number of shares of the company that were sold was 94,500 and the volume of exchange on the New York Stock Exchange was 16 million, what would you expect the price of the stock to be?

Reference no: EM131800001

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