Question

Use the following results obtained from a simple linear regression analysis with 12 observations.

= 37.2895 − (1.2024)*X*

*r*^{2} = .6744*s _{b}* = .2934

Test to determine if there is a significant negative
relationship between the independent and dependent variables at
*α* = .05. Give the test statistic and the resulting
conclusion.

Answer #1

The following needs to be tested:

where \rhoρ corresponds to the population correlation.

The sample size is n = 12 so then the number of degrees of freedom is df = n-2 = 12 - 2 = 10

The corresponding t-statistic to test for the significance of the correlation is:

The p-value is computed as follows:

Since we have that p = 0.9919 ≥0.05, it is concluded that the null hypothesis H0 is not rejected.

Therefore, based on the sample correlation provided, it is concluded that there is not enough evidence to claim that the population correlation ρ is less than 0, at the 0.05 significance level.

A sample of 12 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=77, SST=88, summation (x_i-xbar)2=23,
summation (x_i-xbar)(y_i-ybar)=44.
Calculate the t test statistics to determine whether a
statistically linear relationship exists between x and y.
A sample of 7 observations collected in a regression study on
two variables, x(independent variable) and y(dependent variable).
The sample resulted in the following data.
SSR=24, SST=42
Using a 0.05 level of significance,...

The following table is the output of simple linear regression
analysis. Note that in the lower right hand corner of the output we
give (in parentheses) the number of observations, n, used
to perform the regression analysis and the t statistic for
testing H0: β1 = 0 versus
Ha: β1 ≠ 0.
ANOVA
df
SS
MS
F
Significance F
Regression
1
61,091.6455
61,091.6455
.69
.4259
Residual
10
886,599.2711
88,659.9271
Total
11
947,690.9167
(n = 12;...

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 a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 −
2.3x2 +
7.6x3 +
2.7x4
For this estimated regression equation, SST = 1,835 and SSR =
1,800.
(a)At α = 0.05, test the significance of the
relationship among the variables.State the null and alternative
hypotheses.
-H0: One or more of the parameters is not
equal to zero.
Ha: β0 =
β1 = β2 =
β3 = β4 = 0
-H0:...

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 −
2.3x2 +
7.6x3 +
2.7x4
For this estimated regression equation, SST =
1,805 and SSR = 1,770
a. Find the value of the test
statistic. (Round your answer to two decimal places.)
_________
b. Suppose variables x1 and
x4 are dropped from the model and the following
estimated regression equation is obtained.
ŷ = 11.1 − 3.6x2 + 8.1x3
Compute...

In a regression analysis involving 30 observations, the
following estimated regression equation was obtained.
ŷ = 17.6 + 3.8x1 − 2.3x2 + 7.6x3 + 2.7x4
For this estimated regression equation, SST = 1,815 and SSR =
1,780. (a) At α = 0.05, test the significance of the relationship
among the variables.
State the null and alternative hypotheses.
H0: β0 = β1 = β2 = β3 = β4 = 0
Ha: One or more of the parameters is not equal to...

Upon reviewing the results of a multiple regression involving 30
observations on cross sectional data the Econometric Society
suspected that the variances of the error terms might be related to
the predicted values of the dependent variable. Alarmed by the
prospects they quickly ran a simple regression yielding the
following results:
ei2 = 10.956 + 3.068?̂? R2 = 0.096
Using hypothesis testing, test at a 5% level to see if the variance
of error terms is related to the predicted...

An application of the simple linear regression model generated
the following results involving the F test of the overall
regression model: p = 0.0012, R2 = 0.67. The null hypothesis, which
states that none of the predictor variables are statistically
significantly related to the outcome variable, should be
rejected.
True
False

You estimate a simple linear regression model using a sample of
25 observations and obtain the following results (estimated
standard errors in parentheses below coefficient estimates): y =
97.25 + 19.74 *x
(3.86) (3.42)
You want to test the following hypothesis: H0: beta2 = 1, H1:
beta2 >12. If you choose to reject the null hypothesis based on
these results, what is the probability you have committed a Type I
error?
a.)between .01 and .02 b.)between .02 and .05 c.)less...

In a simple linear regression model, if the independent and
dependent variables are negatively linearly related, then the
standard error of the estimate will also be negative.

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