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goblinko [34]
3 years ago
11

In a multiple regression equation, two independent variables are considered, and the sample size is 30. The regression coefficie

nts and the standard errors are as follows.
b1 = 2.815 Sb1 = 0.75
b2 = -1.249 Sb2 = 0.41
Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the .05 significance level. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)

H0: β1 = 0 H0: β2 = 0
H1: β1 ≠ 0 H1: β2 ≠ 0
H0 is rejected if t < -2.042 or t > 2.042
t for b1 coefficient =
t for b2 coefficient =
(Click to select)Neither the first nor secondThe first and secondThe second variable can be deleted.
Mathematics
1 answer:
MAXImum [283]3 years ago
7 0

Answer:

Both the variables are important for the regression analysis and cannot be deleted.

Step-by-step explanation:

(1)

The hypothesis for for the testing of coefficient β₁ are:

<em>H</em>₀: β₁ = 0 vs. <em>H</em>ₐ: β₁ ≠ 0

The test statistic is:

t=\frac{b_{1}}{S_{b_{1}}} =\frac{2.815}{0.75}= 3.753

It is provided that H₀ is rejected if <em>t</em> > 2.042.

The test statistic value, <em>t</em> = 3.753 > 2.042.

Thus, the null hypothesis is rejected.

<u>Conclusion:</u>

There is a significant relationship between the regression variable and the dependent variable.

(2)

The hypothesis for for the testing of coefficient β₂ are:

<em>H</em>₀: β₂ = 0 vs. <em>H</em>ₐ: β₂ ≠ 0

The test statistic is:

t=\frac{b_{2}}{S_{b_{2}}} =\frac{-1.249}{0.41}= -3.046

It is provided that H₀ is rejected if <em>t</em> < -2.042.

The test statistic value, <em>t</em> = -3.046 < -2.042.

Thus, the null hypothesis is rejected.

<u>Conclusion:</u>

There is a significant relationship between the regression variable and the dependent variable.

Thus, both the variables are important for the regression analysis and cannot be deleted.

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