Question

Complete the following ANOVA table for a multiple linear regression model and answer the following questions.

Source | df | SS | MS | F |
---|---|---|---|---|

Regression | 93 | |||

30 | ||||

Total | 33 | 267 |

a) How many independent variables are included in the model?

b) State the null and alternate hypothesis to be tested.

c) At a 0.01 level of significance, is the multiple linear regression model significant? (Justify)

d) How many data points have been collected?

Answer #1

Source | df | SS | MS | F |

Regression | 3 | 93 | 31 | 5.345 |

Error | 30 | 174 | 5.8 | |

Total | 33 | 267 |

a)

There are three independent variables are included in the model.

b)

The null and alternative hypothesis

H1: At least one of are not the same.

c)

Level of significance = 0.01

Test statistic F = 5.345

Degrees of freedom are: 3, 30

Critical value = 4.510

( From f table)

Test statistic > critical value we reject the null hypothesis.

Conclusion: The multiple linear regression model significant.

d)

Data points are: 33+ 1 = 34

Complete the following ANOVA table for a multiple linear
regression model and answer the following questions.
Source
df
SS
MS
F
Regression
93
30
Total
33
267
a) How many independent variables are included in the model?
b) State the null and alternate hypothesis to be tested.
c) At a 0.01 level of significance, is the multiple linear
regression model significant? (Justify)
d) How many data points have been collected?

Complete the ANOVA
summary table below. In addition, answer the following questions
for the ANOVA summary table.
a. What is the
factorial notation?
b. How many conditions
were in the study?
c. How many subjects
were in the study?
d. Identify
significant main effects and interaction effects.
Source
df SS MS F
A 2 40
B 3 60
A x B 6 150
Error 72
Total 83 400

Use the information and general form of the ANOVA table for
multiple regression from class or from page 613 of the book to
complete the table, find the F-statistic, and find R2.
Source
DF
SS
MS
F
Model
4
70
Error
Total
33
524
For question 17, what percentage of the variation in the
response variable is explained by the explanatory variables?
(report as %)
What is the range for the p-value for question 17?
>0.100
0.050 to 0.100
0.025...

A linear regression analysis was carried out and from the sample
data, the partially filled ANalysis Of VAriance (ANOVA) given in
part (a) was obtained. Based on it, answer the following:
==========
a)
Complete the ANalysis Of VAriance (ANOVA) table below.
Source Source
df df
SS SS
MS MS
Regression (Model) Regression (Model)
11
86.5986.59
19.930319.9303
Residual Error Residual Error
2828
Total Total
2929
208.24208.24
--------
b)
The regression standard error, s=s=
--------
c)
To test H0:β1=0H0:β1=0 based on the given
information,
the value of...

3. Refer to the following ANOVA Summary Table
to answer the questions listed below it.
SOURCE
SS
df
MS
F
Between
23.57
3
.
Within
24
.95
Total
46.43
Answer each of these questions concerning this ANOVA
Summary Table:
What is SS within?
Your Answer:
.
What is MS between?
Your Answer:
.
What is df total?
Your Answer:
.
What is the observed...

Explain the difference between simple and multiple linear
regression.
A. Simple linear regression is faster
B. The difference is in how many independent variables used in
the regression model
C. There is no difference
D. There is a difference in the linearity

Use the multiple regression output shown to answer the following
questions.
The regression equation is
Y=9.40+0.332X1+0.067X2-0.251X3
Predictor
Coef
SE Coef
T
P
Constant
9.395
6.858
1.37
0.184
X1
0.3316
0.8962
0.37
0.716
X2
0.0666
-0.0520
-1.28
0.214
X3
-0.2508
-0.1036
2.42
0.025
S=4.84768
R-Sq=15.0%
R-Sq(adj)=2.8%
Analysis of Variance
Source
DF
SS
MS
F
P
Regression
3
86.8
28.93
1.23
0.322
Residual Error
21
493.5
23.5
Total
24
580.3
a) Which variable might we try eliminating first to possibly
improve this...

Complete the following ANOVA summary table for a model, where
there are four levels of factor A selected at random and three
levels of factor B selected at random. Each cell of the design
includes 20 students (α = .05).
Also, in statistical language (symbols) what is the most
appropriate null and alternative hypothesis for each factor
(effect) for the model?
Source
SS
DF
MS
F
CriticalValue
Decision
η2
ω2
A
12
B
22
AB
Within
114
Total
172

Complete the following ANOVA summary table for a model, where
there are four levels of factor A selected at random and three
levels of factor B selected at random. Each cell of the design
includes 20 students (α = .05).
Also, in statistical language (symbols) what is the most
appropriate null and alternative hypothesis for each factor
(effect) for the model?
Source
SS
DF
MS
F
CriticalValue
Decision
η2
ω2
A
12
B
22
AB
Within
114
Total
172

Does the correlation among the independent variables post a
problem in a multiple linear regression model? Explain

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