Question

A computer analysis of 5 pairs of observations results in the least-squares regression equation y = 2.9091 + 3.0909x, and the standard deviation of the slope is listed as sb1 = 0.886. At α = 0.05, can we conclude that the slope of the regression line, β1, is zero? Use the standard five-step hypothesis testing procedure. Make sure that your last statement is a common sense one. (The final calculated value of t shall be rounded to 4 places to the right of the decimal point and underlined.)

Answer #1

A computer analysis of 5 pairs of observations results in the
least-squares regression equation y = 2.9091 + 3.0909x, and the
standard deviation of the slope is listed as sb1 = 0.886. At α =
0.05, can we conclude that the slope of the regression line, β1, is
zero? Use the standard five-step hypothesis testing procedure. Make
sure that your last statement is a common sense one. (The final
calculated value of t shall be rounded to 4 places to...

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 27 observations, the
following estimated regression equation was developed. ŷ =
25.2 + 5.5x1 For this estimated
regression equation SST = 1,550 and SSE = 530.
(a) At α = 0.05, test whether
x1 is significant.State the
null and alternative hypotheses.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β0 ≠ 0
Ha: β0 =
0
H0: β0 = 0
Ha: β0 ≠ 0
H0: β1 = 0
Ha: β1 ≠ 0
Find the value...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
x1is significant.State the null and
alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠ 0
H0: β0 ≠ 0
Ha: β0 =
0
H0: β1 ≠ 0
Ha: β1 = 0
H0: β1 = 0
Ha: β1 ≠ 0
Find the value...

In a regression analysis involving 27 observations, the
following estimated regression equation was developed.
ŷ = 25.2 + 5.5x1
For this estimated regression equation SST = 1,600 and SSE =
550.
(a) At α = 0.05, test whether
x1 is significant.
State the null and alternative hypotheses.
H0: β0 = 0
Ha: β0 ≠
0H0: β0 ≠ 0
Ha: β0 =
0 H0:
β1 ≠ 0
Ha: β1 =
0H0: β1 = 0
Ha: β1 ≠ 0
Find the value of...

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...

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:...

The estimated
regression equation for a model involving two independent variables
and 55 observations is:
y-hat = 55.17 +
1.1X1 - 0.153X2
Other statistics produced for analysis
include:
SSR = 12370.8
SST = 35963.0
Sb1 = 0.33
Sb2 = 0.20
Interpret b1 and b2 in this estimated regression equation
b. Predict y when X1 = 55 and X2 =
70.
Compute R-square and Adjusted R-Square.
e. Compute MSR and MSE.
f. Compute F and use it to test
whether the...

The following estimated regression equation based on 10
observations was presented.
ŷ = 21.1370 + 0.5509x1 +
0.4980x2
Here, SST = 6,724.125, SSR = 6,222.375,
sb1 =
0.0814, and
sb2 =
0.0565.
1. Compute MSR and MSE. (Round your answers to three decimal
places.)
MSR=
MSE=
2. Compute F and perform the appropriate F
test. Use α = 0.05.
2a. State the null and alternative hypotheses.
(a) H0: β1 =
β2 = 0
Ha: One or more of the parameters...

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;...

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