Question
In: Statistics and Probability
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow....
Data on advertising expenditures and revenue (in thousands of dollars) for the Four Seasons Restaurant follow. Advertising Expenditures Revenue 1 20 2 33 4 44 6 40 10 52 14 53 20 54
a. Let X equal advertising expenditures and Y equal revenue. Complete the estimated regression equation below (to 2 decimals). y =( )+( )x b. Compute the following (to 1 decimal). SSE ( ) SST ( ) SSR ( )MSR ( ) MSE ( )
c. Test whether revenue and advertising expenditures are related at a .05 level of significance. Compute the F test statistic ( to 2 decimals).
Solutions
Expert Solution
| x | y | (x-xbar)^2 | (y-ybar)^2 | (x-xbar)*(y-ybar) | |
| 1 | 20 | 51.020408 | 496.65306 | 159.1836735 | |
| 2 | 33 | 37.734694 | 86.22449 | 57.04081633 | |
| 4 | 44 | 17.163265 | 2.9387755 | -7.102040816 | |
| 6 | 40 | 4.5918367 | 5.2244898 | 4.897959184 | |
| 10 | 52 | 3.4489796 | 94.367347 | 18.04081633 | |
| 14 | 53 | 34.306122 | 114.79592 | 62.75510204 | |
| 20 | 54 | 140.59184 | 137.22449 | 138.8979592 | |
| sum | 57 | 296 | 288.85714 | 937.42857 | 433.7142857 |
| mean | 8.142857143 | 42.28571429 | sxx | syy | sxy |
| slope=b1=sxy/sxx | 1.50148368 | ||||
| intercept=b0=ybar-(slope*xbar) | 30.05934718 | ||||
| SST | SYY | 937.42857 | |||
| SSR | sxy^2/sxx | 651.21492 | |||
| SSE | syy-sxy^2/sxx | 286.21365 |
The Fitted model is
y=30.1+1.50(Expenditure)
Ansb:
SSE=286.22
SST=937.43
SSR=651.21
#MSR=SSR/1=651.21
#MSE=SSE/(n-2)=57.24273
| ANOVA | |||||
| df | SS | MS | F | ||
| Regression | 1 | 651.2149216 | 651.2149 | 11.37638 | |
| Residual | (n-2)=5 | 286.2136499 | 57.24273 | ||
| Total | 6 | 937.4285714 |
Ansc:
F-statistics=MSR/MSE=11.38
F-critical=6.608----using FINV(0.05,1,5)
P-value=0.0074
#P-value<0.05 hence we reject the null hypothesis at 5% l.o.s
#we reject the H0. Hence claim is significant
orchestra answered 2 years agoRelated Solutions
The following data gives the monthly sales (in thousands of dollars) for different advertising expenditures (also...
The following data gives the monthly sales (in thousands of
dollars) for different advertising expenditures (also in thousands
of dollars) and sales commission percentages.
Sales
245 138 352
322 228
275 560
366
Advertising
16.5
18.0 22.3
18.4 19.0 19.5
30.0 18.6
Commission
10.5 2.0
4.0
3.5 4.5
1.8
9.0 8.5
What amount of sales would...
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
Weekly
Television
Newspaper
Gross Revenue
Advertising
Advertising
($1,000s)
($1,000s)
($1,000s)
100
5.0
1.5
90
2.0
2.0
95
4.0
1.5
92
2.5
2.5
103
3.0
3.3
94
3.5
2.3
94
2.5
4.2
94
3.0
2.5
Develop an estimated regression equation with the amount of television advertising as the independent variable (to 1...
The chart below lists the sales in thousands of dollars based on the advertising budget for...
The chart below lists the sales in thousands of dollars based on
the advertising budget for that quarter. The regression equation is
Y' = 4.073 + 0.8351X. What is the correlation
coefficient?
Advertising ($hunderds)
Sales ($thousands)
0
5
3
5.5
4
7
5
7.8
6
9
7
11
Multiple Choice
0.775
0.844
0.926
1.00
David's Landscaping has collected data on home values (in thousands of $) and expenditures (in thousands...
David's Landscaping has collected data on home values (in
thousands of $) and expenditures (in thousands of $) on landscaping
with the hope of developing a predictive model to help marketing to
potential new clients. Data for 14 households may be found in the
file Landscape.
Home
Value
($1,000)
Landscaping
Expenditures
($1,000)
242
8.1
321
10.8
198
12.2
340
16.2
300
15.6
400
18.9
800
23.5
200
9.5
521
17.5
547
22.0
437
12.1
464
13.5
635
17.9
356
13.9...
David's Landscaping has collected data on home values (in thousands of $) and expenditures (in thousands...
David's Landscaping has collected data on home values (in
thousands of $) and expenditures (in thousands of $) on landscaping
with the hope of developing a predictive model to help marketing to
potential new clients. Data for 14 households may be found in the
file Landscape.
Home
Value
($1,000)
Landscaping
Expenditures
($1,000)
242
8.1
321
10.8
198
12.2
340
16.2
300
15.6
400
18.9
800
23.5
200
9.5
521
17.5
547
22.0
437
12.1
464
13.5
635
17.9
356
13.9...
the following are the monthly sales (in thousands of dollars) for a company in four regions...
the following are the monthly sales (in thousands of dollars)
for a company in four regions of the country.
North
East
South
West
34
28
18
24
47
36
30
38
44
40
30
41
29
21
30
24
37
23
Does the data suggest that there is a difference in the mean
monthly sales among the different regions?
A restaurant manger, Coleman, at the Four Seasons Hotel wants to predict/forecast a number of meals...
A restaurant manger, Coleman, at the Four Seasons Hotel wants to
predict/forecast a number of meals to be prepared for the breakfast
since the labor costs and cost of good sold are vey high and does
not want to create high volume of waste and manage the inventory in
a proper way.
He looks through the previous data (2016) to determine the
relationship between the number of guest stayed at the hotel and
number of meals served from the following...
The following data give the annual incomes (in thousands of dollars) and amounts (in thousands of dollars) of life insurance policies for eight persons.
The following data give the annual incomes (in thousands of dollars) and amounts (in thousands of dollars) of life insurance policies for eight persons.(a) At the 98% confidence level, test whether annual income and the amount of life insurance policies are independent.(b) Find the attained significance level.(c) State any assumptions you have made in solving the problem.
The total revenue, in thousands of dollars, from the sale of x spas and y solar...
The total revenue, in thousands of dollars, from the sale of x
spas and y solar heaters is approximated by R(x,y)=
12+74x+85y-3x^2-5y^2-5xy.
find the number of each that should be sold to procude maximum
revenue. Find the maximum revenue.
The payoff table below provides the profits (in thousands of dollars) for each of four alternatives...
The payoff table below provides the profits (in thousands of
dollars) for each of four alternatives in each of three
supplies.
Supplies
Alternative
S1
S2
S3
A1
112
67
-26
A2
82
85
101
A3
85
72
80
A4
-50
90
110
Suppose that the probabilities for the supplies above are
P(S1) = 0.6,
P(S2) = 0.2, and
P(S3) = 0.1.
Which alternative should be selected under Bayes’ Rule?
What is the expected value of perfect information for this
decision?
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Explain how biology, culture, and their interaction shape sex differences.
- Write a program that computes the tax and tip on a restaurant bill for a patron...
- clear all close all % %*******Parameter Settings******** %********************************* Fs=8192; %Sampling frequency (MATLAB's default) Ts=1/Fs; %Sampling time...
- Name a business that you believe has experienced declining costs attributable to computerization. Were variable costs...
- With C++, 1. Assume we use two linked lists that represent Set A and Set B...
- A beam of light shines on an equilateral glass prism at an angle of 45∘ to...
- This is an intro to python question. #Write a function called search_for_string() that takes two #parameters,...
ADVERTISEMENT