Consider the data.
x_{i} |
2 | 6 | 9 | 13 | 20 |
---|---|---|---|---|---|
y_{i} |
5 | 16 | 8 | 24 | 23 |
(a)
What is the value of the standard error of the estimate? (Round your answer to three decimal places.)
(b)
Test for a significant relationship by using the t test. Use α = 0.05.
State the null and alternative hypotheses.
H_{0}: β_{0} ≠ 0
H_{a}: β_{0} = 0
H_{0}: β_{1} ≠ 0
H_{a}: β_{1} =
0
H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
H_{0}: β_{0} = 0
H_{a}: β_{0} ≠ 0
H_{0}: β_{1} ≥ 0
H_{a}: β_{1} < 0
Find the value of the test statistic. (Round your answer to three decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
Do not reject H_{0}. We conclude that the relationship between x and y is significant.
Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
Reject H_{0}. We cannot conclude that the relationship between x and y is significant.
Reject H_{0}. We conclude that the relationship between x and y is significant.
(c)
Use the F test to test for a significant relationship. Use α = 0.05.
State the null and alternative hypotheses.
H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
H_{0}: β_{1} ≥ 0
H_{a}: β_{1} <
0
H_{0}: β_{0} = 0
H_{a}: β_{0} ≠ 0
H_{0}: β_{0} ≠ 0
H_{a}: β_{0} = 0
H_{0}: β_{1} ≠ 0
H_{a}: β_{1} = 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 =
What is your conclusion?
Reject H_{0}. We conclude that the relationship between x and y is significant.
Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
Reject H_{0}. We cannot conclude that the relationship between x and y is significant.
Do not reject H_{0}. We conclude that the relationship between x and y is significant.
Using Excel, go to Data, select Data Analysis, choose Regression.
SUMMARY OUTPUT | |||||
Regression Statistics | |||||
Multiple R | 0.803 | ||||
R Square | 0.645 | ||||
Adjusted R Square | 0.526 | ||||
Standard Error | 5.910 | ||||
Observations | 5 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 1 | 190 | 190.000 | 5.439 | 0.1019 |
Residual | 3 | 104.8 | 34.933 | ||
Total | 4 | 294.8 | |||
Coefficients | Standard Error | t Stat | P-value | ||
Intercept | 5.2 | 5.037 | 1.032 | 0.3778 | |
X | 1 | 0.429 | 2.332 | 0.1019 |
a) Standard error = 5.910
b) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
Test statistic = 2.332
p-value = 0.1019
Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
c) H_{0}: β_{1} = 0
H_{a}: β_{1} ≠ 0
Test statistic = 5.44
p-value = 0.102
Do not reject H_{0}. We cannot conclude that the relationship between x and y is significant.
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