Question

Explain why a multiple regression analysis reported an F statistic with a p < 0.05 but none of the individual coefficients were significant.

Answer #1

**Solution:** In multiple regression analyses, we
can see the results are statistically significant using the
F-statistic but none of the individual coefficients are
significant. The reason for such results is that the F-test tests
the overall significance of the model and individual t-test tests
the significance of the individual significance of the coefficient.
Therefore, F-test determines that the coefficients are jointly not
all equal to zero, while the individual t-tests determine that all
of them are individually not equal to zero.

Suppose that in a multiple regression the overall model is
significant, but the p values of none of the individual slope
coefficients are small enough. This means that:
a.none of the other choices are correct
b. nonlinear model would be a better fit
c. the assumptions have been violated
d. multicollinearity may be present
e. linear regression would be better

In multiple regression analysis, when we are able to
reject the null hypothesis for the F test, it necessary means that
each variable X has a significant influence over Y? Explain and
justify your answer. (10 points)

A multiple regression
analysis between yearly income (y in $1000s), college
grade point average (x1), age of the
individuals (x2), and gender of the individual
(x3; 0 representing female and 1 representing
male) was performed on a sample of 10 people, and the following
results were obtained using Excel:
ANOVA
df
SS
MS
F
Regression
360.59
Residual
23.91
Coefficients
Standard
Error
Intercept
4.0928
1.4400
x1
10.0230
1.6512
x2
0.1020
0.1225
x3
-4.4811
1.4400
We want to test
whether or not...

A multiple regression was run to
explain CEO compensation (in $ per year) of major Northwest firms
using three explanatory variables: the number of Employees,
MarketCap (market capitalization in $thousands), and NetIncome (in
$thousands). The prediction equation was
CEOComp = 6,260,416 + 29.167*Employees
- 0.06309*MarketCap + 2.5617*NetIncome
Furthermore, the
F-test had F = 7.32 with a p-value of
0.000333, the t-test for Employees had a p-value
of 0.208, the t-test for MarketCap had a p-value
of 0.040, and the...

The following results were obtained as part of a multiple
regression analysis involving 3 independent variables:
SSR = 11440 SSYY = 16781
and n = 28
What is the value of the calculated F statistic?
What is the critical value for the model test if alpha =
0.05?
What is the value of the coefficient of determination?
What is the value of the standard error of the estimate?
What is the value of adjusted R2?
What are the total number...

In a multiple regression analysis, k = 5 and n
= 21, the MSE value is 3.58, and SS total is 498.46. At the 0.05
significance level, can we conclude that any of the regression
coefficients are not equal to 0? (Round your answers to 2
decimal places.)
H0: β1 = β2 =
β3 = β4 = β5 = 0
H1: Not all β's equal zero.
Complete the following ANOVA table.

Regression Analysis with a Minitab output
Assume that your company owns multiple retail outlets in cities
across the United States. You conduct a study to determine if daily
sales levels (in hundreds of dollars) can be predicted by the
number of competitors that are located within a one-mile radius of
each location and city population (in thousands of people).
Therefore, the dependent variable is SALES and the two independent
variables are NUMBER OF COMPETITORS and CITY POPULATION. Your
research team...

Exhibit 16-1
In a regression analysis involving 25 observations, the following
estimated regression equation was developed.
Y=10 - 18X1+ 3X2 + 14X3
Also, the following standard errors and the sum of squares were
obtained.
Sb1 = 3
Sb2 = 6
Sb3 = 7
SST = 4,800
SSE = 1,296
Refer to Exhibit 16-1. If you want to determine whether or not the
coefficients of the independent variables are significant, the
critical value of t statistic at α = 0.05 is...

In testing the validity of a multiple regression model, a large
value of the F-test statistic indicates that:
a.
most of the variation in the independent variables is explained
by the variation in y
b.
the model provides a poor fit
c.
most of the variation in y is explained by the
regression equation and the model provides a poor fit
d.
most of the variation in y is explained by the
regression equation
e.
most of the variation in...

The following multiple regression printout can be used to
predict a person's height (in inches) given his or her shoe size
and gender, where gender = 1 for males and 0 for females.
Regression Analysis: Height Versus Shoe Size,
Gender
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
Constant
55.22
1.06
52.09
0.000
Shoe Size
1.163
0.18
0.000
Gender
2.572
0.489
5.26
0.000
(a)
Find the value of the test statistic for shoe size. (Round your
answer to two decimal places.)...

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