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
orchestra answered 2 years ago
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