Question

Consider the following data for a dependent variable y and two independent variables, x₁ and x₂.

x1	x2	y
30	12	95
47	10	108
25	17	112
51	16	178
40	5	94
51	19	175
74	7	170
36	12	117
59	13	142
76	16	212

The estimated regression equation for these data is

ŷ = −18.52 + 2.01x₁ + 4.75x₂.

Here, SST = 15,234.1, SSR = 14,109.8, s_b1 = 0.2464, and s_b2 = 0.9457.

(a)Test for a significant relationship among x₁, x₂, and y. Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.H₀: β₁ < β₂
H_a: β₁ ≥ β₂    H₀: β₁ ≠ 0 and β₂ = 0
H_a: β₁ = 0 and β₂ ≠ 0H₀: β₁ > β₂
H_a: β₁ ≤ β₂H₀: β₁ ≠ 0 and β₂ ≠ 0
H_a: One or more of the parameters is equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.Reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.    Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship among the variables.Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship among the variables.

(b)Is β₁ significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₁ < 0
H_a: β₁ ≥ 0    H₀: β₁ = 0
H_a: β₁ > 0H₀: β₁ > 0
H_a: β₁ ≤ 0H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence to conclude that β₁ is significant.Reject H₀. There is insufficient evidence to conclude that β₁ is significant.    Do not reject H₀. There is insufficient evidence to conclude that β₁ is significant.Do not reject H₀. There is sufficient evidence to conclude that β₁ is significant.

(c)Is β₂ significant? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₂ ≠ 0
H_a: β₂ = 0H₀: β₂ > 0
H_a: β₂ ≤ 0    H₀: β₂ = 0
H_a: β₂ ≠ 0H₀: β₂ = 0
H_a: β₂ > 0H₀: β₂ < 0
H_a: β₂ ≥ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Reject H₀. There is sufficient evidence to conclude that β₂ is significant.    

Do not reject H₀. There is insufficient evidence to conclude that β₂ is significant.

Do not reject H₀. There is sufficient evidence to conclude that β₂ is significant.

Answer 1