Consider the following data for a dependent variable y and two independent variables, x_{1}and x_{2}.
x_{1} |
x_{2} |
y |
---|---|---|
30 | 12 | 96 |
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 | 211 |
The estimated regression equation for these data is ŷ = −17.33 + 2.00x_{1} + 4.73x_{2}.
Here, SST = 15,002.1, SSR = 13,887.5, s_{b1} = 0.2454,and s_{b2} = 0.9417.
(a)Test for a significant relationship among x_{1}, x_{2}, and y. Use α = 0.05.State the null and alternative hypotheses.
(b)Find the value of the test statistic. (Round your answer to two decimal places.)
(c)Find the p-value. (Round your answer to three decimal places.)
(d)State your conclusion.
-Reject H_{0}. There is sufficient evidence to conclude that there is a significant relationship among the variables.
-Reject H_{0}. There is insufficient evidence to conclude that there is a significant relationship among the variables.
-Do not reject H_{0}. There is insufficient evidence to conclude that there is a significant relationship among the variables
-Do not reject H_{0}. There is sufficient evidence to conclude that there is a significant relationship among the variables.
(e) Is β_{1} significant? Use α = 0.05.State the null and alternative hypotheses.
(f) Find the value of the test statistic. (Round your answer to two decimal places.)
(g) Find the p-value. (Round your answer to three decimal places.)
(h)State your conclusion.
-Do not reject H_{0}. There is sufficient evidence to conclude that β_{1} is significant.
-Reject H_{0}. There is insufficient evidence to conclude that β_{1} is significant.
-Do not reject H_{0}. There is insufficient evidence to conclude that β_{1} is significant.
-Reject H_{0}. There is sufficient evidence to conclude that β_{1} is significant.
(i) Is β_{2} significant? Use α = 0.05. State the null and alternative hypotheses.
(j) Find the value of the test statistic. (Round your answer to two decimal places.)
(k)Find the p-value. (Round your answer to three decimal places.)
(L) State your conclusion.
-Do not reject H_{0}. There is sufficient evidence to conclude that β_{2} is significant.
-Reject H_{0}. There is insufficient evidence to conclude that β_{2} is significant.
-Do not reject H_{0}. There is insufficient evidence to conclude that β_{2} is significant
-Reject H_{0}. There is sufficient evidence to conclude that β_{2} is significant.
Ho: ß1=ß2 =0 |
Ha:at least one ßi is not equal to 0 |
b_)
p=number of independent variables= | 2 | ||||
MSR =SSR/p = | 6943.750 | ||||
MSE=(SSE/(n-p-1))= | 159.229 | ||||
F test statistic =MSR/MSE= | 43.61 |
c) p value =0.000
d) -Reject H_{0}. There is sufficient evidence to conclude that there is a significant relationship among the variables.
e_)
Ho: ß1=0
Ha:ß10
f)
value of the test statistic =2/0.2454 =8.15 (please try 8.13 if this comes wrong)
g) p value =0.000
h) -Reject H_{0}. There is sufficient evidence to conclude that β_{1} is significant.
i)
Ho: ß2=0
Ha:ß20
j)
value of the test statistic =4.73/0.9417 =5.02
k)
p value =0.002
l) -Reject H_{0}. There is sufficient evidence to conclude that β_{2} is significant.
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