In: Math
You may need to use the appropriate technology to answer this question.
Consider the following data for a dependent variable y and two independent variables,
x1
and
x2.
x1 |
x2 |
y |
---|---|---|
30 | 12 | 93 |
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 | 210 |
The estimated regression equation for these data is
ŷ = −18.21 + 2.01x1 + 4.72x2.
Here, SST = 15,134.9, SSR = 13,994.6,
sb1 = 0.2482,
and
sb2 = 0.9524.
(a)
Test for a significant relationship among
x1, x2, and y.
Use α = 0.05.
State the null and alternative hypotheses.
H0: β1 >
β2
Ha: β1 ≤
β2H0:
β1 = β2 = 0
Ha: One or more of the parameters is not equal
to zero. H0:
β1 ≠ 0 and β2 ≠ 0
Ha: One or more of the parameters is equal to
zero.H0: β1 ≠ 0 and
β2 = 0
Ha: β1 = 0 and
β2 ≠ 0H0:
β1 < β2
Ha: β1 ≥
β2
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.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.Reject H0. There is insufficient 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
Ha: β1 ≠
0H0: β1 < 0
Ha: β1 ≥
0 H0:
β1 > 0
Ha: β1 ≤
0H0: β1 = 0
Ha: β1 >
0H0: β1 ≠ 0
Ha: 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 sufficient evidence to conclude that β1 is significant.Do not reject H0. There is insufficient evidence to conclude that β1 is significant.
(c)
Is
β2
significant? Use α = 0.05.
State the null and alternative hypotheses.
H0: β2 < 0
Ha: β2 ≥
0H0: β2 > 0
Ha: β2 ≤
0 H0:
β2 ≠ 0
Ha: β2 =
0H0: β2 = 0
Ha: β2 ≠
0H0: β2 = 0
Ha: 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 sufficient evidence to conclude that β2 is significant.Do not 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.Reject H0. There is insufficient evidence to conclude that β2 is significant.