Question

In: Statistics and Probability

Data from 10 stores in a region of the country are analyzed. Advertising (in hundreds of...

Data from 10 stores in a region of the country are analyzed.
Advertising (in hundreds of dollars),
Employee numbers
Sales (thousands of dollars)

Advertising
8.3
8.6
8.8
10.5
10.7
10.8
11.0
11.0
11.1
11.2
Employees
15
10
8
17
25
28
11
20
25
20
Sales
10.3
10.3
10.2
16.4
18.8
19.7
15.6
18.2
22.6
19.9

1)Find the fitted regression model, which shows that sales are a function of advertising and the number of employees. That is: Sales = f (Advertising, Employees)
2) Do a hypothesis test, using ANOVA, to prove that the variables Advertising and number of employees (together) influence sales. (6 steps)
3) Calculate a 90% confidence interval for sales, in a store that invests $ 840 in advertising and has 12 employees

Solutions

Expert Solution

Descriptive Statistics

Mean

Std. Deviation

N

Sales

16.2000

4.51762

10

Advertising

10.2000

1.15085

10

Employees

17.9000

6.90330

10

On avarge Sales 16.200 (thousands of dollars) , it's mean's that most of sales near to 16.200(thousands of dollars)

On avarge Advertising 10.2000 (in hundreds of dollars) .

On avarge Employees 17.900 number.

Correlations

Sales

Advertising

Employees

Pearson Correlation

Sales

1.000

.921

.849

Advertising

.921

1.000

.643

Employees

.849

.643

1.000

Sig. (1-tailed)

Sales

.

.000

.001

Advertising

.000

.

.022

Employees

.001

.022

.

N

Sales

10

10

10

Advertising

10

10

10

Employees

10

10

10

Above tabel of Sales to Advrtising and Employees are perfect postive linear realtionship.

Variables Entered/Removeda

Model

Variables Entered

Variables Removed

Method

1

Employees, Advertisingb

.

Enter

a. Dependent Variable: Sales

b. All requested variables entered.

Model Summaryb

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Change Statistics

Durbin-Watson

R Square Change

F Change

df1

df2

Sig. F Change

1

.980a

.960

.949

1.02002

.960

84.770

2

7

.000

1.488

a. Predictors: (Constant), Employees, Advertising

96% indicates that the model explains all the variability of the Sales data around its mean, it's mean's that given regression model 96% good fit for given data.

ANOVAa

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

176.397

2

88.198

84.770

.000b

Residual

7.283

7

1.040

Total

183.680

9

Regression model is siginificant for given data ata 0.05 level of alpha

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

90.0% Confidence Interval for B

Correlations

Collinearity Statistics

B

Std. Error

Beta

Lower Bound

Upper Bound

Zero-order

Partial

Part

Tolerance

VIF

1

(Constant)

-14.524

3.330

-4.361

.003

-20.834

-8.214

Advertising

2.509

.386

.639

6.503

.000

1.778

3.241

.921

.926

.489

.586

1.706

Employees

.286

.064

.438

4.453

.003

.165

.408

.849

.860

.335

.586

1.706

a. Dependent Variable: Sales

Regression model:

Sales = -14.524 +2.509 * Adertising + 0.286 * Employees

Now the predict the Sales to dercrease by the -14.524 as per one unit. If Adertising and Employees values are zero then sales of meas is -14.524.

The predict the sales to increase by 2.509   hundreds of dollars Adertising as per one unit of sales.

The predict the sales to increase by 0.286 number of Employees as per one unit of sales.

Coefficient Correlationsa

Model

Employees

Advertising

1

Correlations

Employees

1.000

-.643

Advertising

-.643

1.000

Covariances

Employees

.004

-.016

Advertising

-.016

.149

a. Dependent Variable: Sales

Collinearity Diagnosticsa

Model

Dimension

Eigenvalue

Condition Index

Variance Proportions

(Constant)

Advertising

Employees

1

1

2.927

1.000

.00

.00

.01

2

.069

6.525

.04

.01

.66

3

.004

27.418

.96

.99

.33

a. Dependent Variable: Sales

Residuals Statisticsa

Minimum

Maximum

Mean

Std. Deviation

N

Predicted Value

9.8508

20.5990

16.2000

4.42715

10

Std. Predicted Value

-1.434

.994

.000

1.000

10

Standard Error of Predicted Value

.360

.757

.545

.130

10

Adjusted Predicted Value

9.6669

21.1298

16.2835

4.47181

10

Residual

-.89898

2.10759

.00000

.89958

10

Std. Residual

-.881

2.066

.000

.882

10

Stud. Residual

-1.111

2.340

-.031

1.034

Related Solutions

A certain consumer research firm analyzed the 10​% of adults from a particular region that are...
A certain consumer research firm analyzed the 10​% of adults from a particular region that are either​ "Superbanked" or​ "Unbanked." Superbanked consumers are defined as adults who live in a household that has multiple asset accounts at financial​ institutions, as well as some additional​ investments; Unbanked consumers are adults who live in a household that does not use a bank or credit union. By finding the 5​% of adults that are​ Super banked, the firm identifies financially savvy consumers who...
The revenue equation​ (in hundreds of millions of​ dollars) for barley production in a certain country...
The revenue equation​ (in hundreds of millions of​ dollars) for barley production in a certain country is approximated by R(x)=0.0628x^2+1.435x+2.1958 where x is in hundreds of millions of bushels. Find the​marginal-revenue equation and use it to find the marginal revenue for the production of the given number of bushels. A) The marginal revenue is R'(x)=.........? ​(Round to four decimal places as​ needed.) B) Find the marginal revenue for the production of 200,000,000 bushels. The marginal revenue is ................. hundred million...
Perform a chi-square test to look at the relationship between region of the country (REGION) and...
Perform a chi-square test to look at the relationship between region of the country (REGION) and financial comfort (FCOMFORT). Using alpha = .05, what would you conclude from your test: a. Financial comfort differs depending on the area one lives in. b. People living in less expensive areas are more likely to report that they are financially comfortable. c. There is not a significant relationship between region and financial comfort. d. People living in the northeast region are most likely...
Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected...
Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as: (use sas) Adv Revenue 25 50 15 49.7 20 34 17 30.7 23 27 17 26.3 14 24.6 22 16.9 12 16.7 15 14.6 8 13.8 7 13.2 9 13.1 12 10.6 1 8.8 6 8.7 12 8.5...
Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected...
Problem 2: (Revised 6.3) Magazine Advertising: In a study of revenue from advertising, data were collected for 41 magazines list as follows. The variables observed are number of pages of advertising and advertising revenue. The names of the magazines are listed as: Here is the code help you to paste data into your R: data6<-'Adv Revenue 25 50 15 49.7 20 34 17 30.7 23 27 17 26.3 14 24.6 22 16.9 12 16.7 15 14.6 8 13.8 7 13.2...
explain how data are to be analyzed and interpreted
explain how data are to be analyzed and interpreted
A retail chain has eight stores in a region supplied from four supply sources. Trucks have...
A retail chain has eight stores in a region supplied from four supply sources. Trucks have a capacity of 40,000 units and cost $1,000 per load plus $100 per delivery. Thus, a truck making two deliveries charges $1,200. The cost of holding one unit in inventory at retail for a year is $0.20. • The vice president of the supply chain is considering whether to use direct shipping from suppliers to retail stores or setting up milk runs from suppliers...
10 The following data are obtained from DK Stores Inc.’s financial records: 2021 Cost Retail Beginning...
10 The following data are obtained from DK Stores Inc.’s financial records: 2021 Cost Retail Beginning Inventory $75,600 $126,000 Purchases 176,000 244,000 Purchases discount 1,130 Net markups 9,500 Net markdowns 10,625 Normal spoilage 1,200 Sales to customers 215,000 Sales to employees (after 40% employee discounts) 9,705 Price index 1.05 Price indices are based on January 1, 2021 which is the base year. Suppose DK uses the average cost retail inventory method to account for its inventory. What is the current...
E-ADVERTISING According to i) Effective Language Use in Advertising in the Most Visible Online Stores ii)...
E-ADVERTISING According to i) Effective Language Use in Advertising in the Most Visible Online Stores ii) The Language of Online Advertisements iii) Verbal component of advertisement and the problem of its perception iv) The language of online bank advertisements in English prepare a memo (follow memo format) to your supervisor Mr. Richardson from Advertising Unit on Language Concerns and Tips for Online Advertising.
the data on ages (in years) and prices (in hundreds of dollars) for 8 cars of...
the data on ages (in years) and prices (in hundreds of dollars) for 8 cars of a specific model are given: Age: 8 3 6 9 2 5 6 3 price: 45 210 100 33 267 134 109 235 Fund the linear correlation coefficient r. Use appropriate test to indicate if there is a linear correlation.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT