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...

Assume you ran a multiple regression to gain a better
understanding of the relationship between lumber sales, housing
starts, and commercial construction. The regression uses lumber
sales (in $100,000s) as the response variable with housing starts
(in 1,000s) and commercial construction (in 1,000s) as the
explanatory variables. The estimated model is Lumber Sales =
β0 +β1Housing Starts +
β2 Commercial Constructions + ε. The
following ANOVA table summarizes a portion of the regression
results.
df
SS
MS
F
Regression
2...

X Y 1 50 8 57 11 43 16 18 20 18 Use the estimated regression
equation is y = 61.5 – 2.21x. A). Compute the Mean Square Error
Using Equation. S^2 = MSE = SSE/(n-2) B). Compute The Standard
Error of the estimate using equation. S = SQRT(MSE) =
SQRT[SSE/(n-2)] C). Compute the estimated Standard Deviation of b1
using equation. Sb1 = S/SQRT[SUM(x-(x-bar))^2] D). Use the t-test
to test the following hypothesis (α = 0.05) H0: β1 = 0...

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 =...

Use Excel to develop a regression model for the Hospital
Database (using the “Excel Databases.xls” file on Blackboard) to
predict the number of Personnel by the number of Births. Perform a
test of the slope. What is the value of the test statistic? Write
your answer as a number, round your answer to 2 decimal places.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.697463374
R
Square
0.486455158
Adjusted R Square
0.483861497
Standard Error
590.2581194
Observations
200
ANOVA
df
SS
MS
F...

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...

It has been speculated that there is a linear
relationship between Oxygen and Hydrocarbon Levels. Specifically,
Oxygen purity is assumed to be dependent on Hydrocarbon levels. A
linear regression is performed on the data in Minitab, and you get
the following results:
Regression Analysis: Purity-y versus Hydrocarbon
level-X
Predictor
Coef SE Coef
T P
Constant
74.283 1.593 46.62 0.000
Hydrocarbon level-X 14.947 1.317 11.35
0.000
S = 1.08653 R-Sq = 87.7% R-Sq(adj) =
87.1%
Analysis of Variance
Source
DF SS ...

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