Regression using SPSS – A suburban hotel derives its gross income from its hotel and restaurant operations.

admin — Thu, 29 Jul 2010 15:21:00 +0000

A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied.

Day	Income	Occupied
1	$1,452	23
2	1,361	47
3	1,426	21
4	1,470	39
5	1,456	37
6	1,430	29
7	1,354	23
8	1,442	44
9	1,394	45
10	1,459	16
11	1,399	30
12	1,458	42
13	1,537	54
14	$1,425	27
15	1,445	34
16	1,439	15
17	1,348	19
18	1,450	38
19	1,431	44
20	1,446	47
21	1,485	43
22	1,405	38
23	1,461	51
24	1,490	61
25	1,426	39

Use a statistical software package to answer the following questions.

a. Does the breakfast revenue seem to increase as the number of occupied rooms increases? Draw a scatter diagram to support your conclusion.

b. Determine the coefficient of correlation between the two variables. Interpret the value.

c. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.

d. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?

Answer

(A)

(B)
r = 0.44, there is a WEAK positive correlation.
(C)
df = n-2 = 25-2 = 23
α = 0.05
one-tailed critical value T = 1.319
Test statistic T = r*Sqrt[(n-2)/(1-r²)] = 0.44*Sqrt[(25-2)/(1-0.44²)] = 2.35
Conclusion: Since 2.35 > 1.319 we conclude that there is a positive relationship between the variables.
(D)
r² = 0.44² = 0.1936, so approximately 19% of the variation in revenue is explained by the variation in the number of rooms occupied.

Coins, dice, probability

admin — Sun, 09 May 2010 13:40:00 +0000

1)Three dice are thrown simultaneously. The probability of obtaining a sum of 6 is?

1)1/24 2)5/108 3)1/54 4)7/216

2)A coin is tossed 3 times. The probability of getting head and tail alternately is?

1)1/6 2)1/8 3)1/4 4)1/3

3)Three dice are thrown simultaneously. The probability of obtaining a multiple of 5?

1)1/36 2)5/108 3)1/54 4)43/216

Answer：

1）

6=1+1+4，3 possible outcomes
6=1+2+3，6possible outcomes
6=2+2+2，1possible outcomes
(3+6+1)/6*6*6=10/216 = 5/108

2）Here are the possible outcomes:
HHH, HHT, HTH, HTT, TTT, TTH, THT, THH
There are two outcomes that satisfy the alternate condition HTH and THT. Head and tail come alternatively in these two outcomes,
Total possibilities=8
Number of requirea outcome=2
Probability=2/8=1/4
So number 3) is correct answer

3/）

Maximum of three dice and 18
So that may occur in multiples of 5 to 5,10,15
As and when the 5: 5 = 1 +1 +3 will make arrangement with three kinds of 113
5 = 1 + 2 + 2 will be ordered to do 122 with three kinds of
And the time when 10 of 10 = 1 +3 +6 ordered to do 136 with 6
10 = 1 +4 +5 ordered to do 145 with 6
10 = 2 +2 +6 there are three kinds of ordered to do 226
10 = 2 +3 +5 ordered to do 235 with 6
10 = 2 +4 +4 there are three kinds of ordered to do 244
10 = 3 +3 +4 there are three kinds of ordered to do 334
When and when 15 = 3 +6 +6 15 366 do have three kinds of arrangement
15 = 4 +5 +6 ordered to do 456 with 6
15 = 5 +5 +5 555 ordered to do only one
In summary there and in multiples of 5 3 +3 +3 +6 +6 +6 +6 +3 +3 +3 +1 = 43
The vote occurred a total of three dice combination of a 6 * 6 * 6 = 216
The probability is 43/216 = 43/216