Consider the following data for a dependent variable yand 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

Å· = −18.52 + 2.01x₁ +4.75x₂.

Here, SST = 15,234.1, SSR = 14,109.8,s_b1 =0.2464, ands_b2 =0.9457.

(a)Test for a significant relationship amongx₁, 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 equalto zero.H₀: β₁ <β₂
H_a: β₁ ≥β₂    H₀:β₁ ≠ 0 and β₂ = 0
H_a: β₁ = 0 andβ₂ ≠ 0H₀:β₁ > β₂
H_a: β₁ ≤β₂H₀:β₁ ≠ 0 and β₂ ≠ 0
H_a: One or more of the parameters is equal tozero.

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

=

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence toconclude that there is a significant relationship among thevariables.Reject H₀. There is insufficientevidence to conclude that there is a significant relationship amongthe variables.    Do not rejectH₀. There is insufficient evidence to concludethat there is a significant relationship among the variables.Do notreject H₀. There is sufficient evidence toconclude that there is a significant relationship among thevariables.

(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 twodecimal places.)

=

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

p-value =

State your conclusion.

Reject H₀. There is sufficient evidence toconclude that β₁ is significant.RejectH₀. There is insufficient evidence to concludethat β₁ issignificant.    Do not rejectH₀. There is insufficient evidence to concludethat β₁ is significant.Do not rejectH₀. There is sufficient evidence to concludethat 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 twodecimal places.)

=

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

p-value =

State your conclusion.

Reject H₀. There is insufficient evidence toconclude that β₂ is significant.

Reject H₀. There is sufficient evidence toconclude that β₂ issignificant.    

Do not reject H₀. There is insufficientevidence to conclude that β₂ issignificant.

Do not reject H₀. There is sufficientevidence to conclude that β₂ issignificant.