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

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:

H₀: β₁ = 0 vs. Hₐ: β₁ ≠ 0

The test statistic is:

It is provided that H₀ is rejected if t > 2.042.

The test statistic value, t = 3.753 > 2.042.

Thus, the null hypothesis is rejected.

Conclusion:

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

(2)

The hypothesis for for the testing of coefficient β₂ are:

H₀: β₂ = 0 vs. Hₐ: β₂ ≠ 0

The test statistic is:

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

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

Thus, the null hypothesis is rejected.

Conclusion:

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.

the 4th choice is the correct one

step-by-step explanation:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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