Question

A manager at a company analyzed the relationship between the weekly record sales and factors affecting its sales with a sample of 200 records. The independent variables included in the regression model are as follows: x1: Advertising budget (thousands of dollars), x2: No. of plays on radio per week, x3: Attractiveness of band, The following ANOVA summarizes the regression results.

Table 1: ANOVA

Source of Variation |
df |
Source of Squares |
Mean Square |
F |
R Squared |

Regression |
861377.418 |
0.665 |
|||

Residual or Error |
434574.582 |
||||

Total |
199 |
1295952.0 |

1. What are the degrees of freedom for Regression and Residual, respectively?

2. What are the value of the Regression mean square (MSR) and the Error mean square (MSE), respectively?

3. Evaluate this model with a global test at the 0.05 level of significance. The null hypothesis for this hypothesis test is ________.

4. Compute the global F-statistic for the model.

5. Find F-value for the critical value.

6. State a conclusion.

Answer #1

A manager at a local bank analyzed the relationship between
monthly salary (y, in $) and length of service
(x, measured in months) for 30 employees. She estimates
the model:
Salary = β0 +
β1Service + ε. The following
ANOVA table summarizes a portion of the regression results.
df
SS
MS
F
Regression
1
555,420
555,420
7.64
Residual
27
1,962,873
72,699
Total
28
2,518,293
Coefficients
Standard Error
t-stat
p-value
Intercept
784.92
322.25
2.44
0.02
Service
9.19
3.20
2.87
0.01...

A manager at a local bank analyzed the relationship between
monthly salary (y, in $) and length of service (x, measured in
months) for 30 employees. She estimates the model: Salary = β0 + β1
Service + ε. The following ANOVA table summarizes a portion of the
regression results.
df
SS
MS
F
Regression
1
555,420
555,420
7.64
Residual
27
1,962,873
72,699
Total
28
2,518,293
Coefficients
Standard Error
t-stat
p-value
Intercept
784.92
322.25
2.44
0.02
Service
9.19
3.20
2.87
0.01...

A business is evaluating their advertising budget, and wishes to
determine the relationship between advertising dollars spent and
changes in revenue. Below is the output from their
regression.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.95
R Square
0.90
Adjusted R Square
0.82
Standard Error
0.82
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
3
23.188
7.729
11.505
0.020
Residual
4
2.687
0.672
Total
7
25.875
Coefficients
Std Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
83.91
2.03...

A sales manager for an advertising agency believes there is a
relationship between the number of contacts that a salesperson
makes and the amount of sales dollars earned.
A regression analysis shows the following results:
Coefficients
Standard Error
t Stat
p value
Intercept
−12.201
6.560
−1.860
0.100
Number of contacts
2.195
0.176
12.505
0.000
ANOVA
df
SS
MS
F
Significance F
Regression
1.00
13555.42
13555.42
156.38
0.00
Residual
8.00
693.48
86.68
Total
9.00
14248.90
Additional information needed to perform the...

QUESTION 19
Polynomial regression was used
to predict sales (Y) using advertising expenditure (X) and its
square (X2) as independent variables. The following
information is available:
Predictor
Coefficients
Standard Error
Constant
328.42
29.42
X
10.970
1.832
X2
-.12507
.02586
ANOVA
Source
DF
SS
F
Regression
42.56
Residual
Total
11
14,107.7
Testing, at the .05 level of significance, if the quadratic term is
useful for the prediction of sales, the alternative hypothesis is:
a.
Ha: b1 ¹ 0
b.
Ha: b2 =...

The following data is used to study the relationship between
miles traveled and ticket price for a commercial airline:
Distance in miles:
300 400
450 500
550 600
800 1000
Price charged in $:
140 220
230 250
255 288
350 480
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.987
R Square
0.975
Adjusted R Square
0.971
Standard Error
17.352
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
70291.3
70291.3
233.4
4.96363E-06
Residual
6
1806.6
301.1
Total...

Data needs to be analyzed
For this assignment I have to analyze the regression
(relationship between 2 independent variables and 1 dependent
variable). Below is all of my data and values. I need help
answering the questions that are at the bottom. Questions regarding
the strength of the relationship
Sum of X1 = 184.6
Sum of X2 = 21307.03
Sum of Y = 2569.1
Mean X1 = 3.6196
Mean X2 = 417.7849
Mean Y = 50.3745
Sum of squares (SSX1)...

In models B through D, what seems to be the relationship between
the burglary rate and the percent of the 18-64 population who are
young adults (18-24)?
Select one:
a. It is difficult to describe the relationship; the young adult
variables were all significant at 5% in models B, C, and D, but the
signs and sizes of the coefficients were very different between
models.
b. Conclusions about the relationship between young adults and
the burglary rate are difficult to...

Zenith Computers, Texas would like to predict weekly Internet
sales based on the number of orders. Data (over 15 weeks), relating
the sales volume (in thousands of dollars) to the number of orders
were available. Regression analysis was performed using Excel.
Output related to the regression is given below.
Week
Orders
Sales ($1000)
1
265
15.3
2
150
18.4
3
131
11.6
.
.
.
.
.
.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.795
R Square
0.632
Adjusted R...

A marketing organization wishes to study the effects of four
sales methods on weekly sales of a product. The organization
employs a randomized block design in which three salesman use each
sales method. The results obtained are given in the following
table, along with the Excel output of a randomized block ANOVA of
these data.
Salesman, j
Sales Method,
i
A
B
C
1
40
31
28
2
43
29
23
3
33
22
19
4
32
19
17
ANOVA:...

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