Question
In: Statistics and Probability
You may need to use the appropriate technology to answer this question. Consider the data. xi...
You may need to use the appropriate technology to answer this question.
Consider the data.
|
xi |
2 | 6 | 9 | 13 | 20 |
|---|---|---|---|---|---|
|
yi |
8 | 20 | 11 | 26 | 21 |
(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.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β0 = 0
Ha: β0 ≠ 0
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 ≥ 0
Ha: β1 < 0
H0: β1 = 0
Ha: β1 ≠ 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 =
(c) Use the F test to test for a significant relationship. Use α = 0.05.
State the null and alternative hypotheses.
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 ≠ 0
Ha: β1 = 0
H0: β1 = 0
Ha: β1 ≠ 0
H0: β0 = 0
Ha: β0 ≠ 0
H0: 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 =
Solutions
Expert Solution
Sol:
Peform regression in Excel
Install analysis toolpak in excel and then
Data >Data analysis>regression
Output:
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.646424 | |||||
| R Square | 0.417864 | |||||
| Adjusted R Square | 0.223818 | |||||
| Standard Error | 6.575206 | |||||
| Observations | 5 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 93.1 | 93.1 | 2.153431 | 0.238542 | |
| Residual | 3 | 129.7 | 43.23333 | |||
| Total | 4 | 222.8 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 10.2 | 5.603664 | 1.820238 | 0.166281 | -7.63336 | 28.03336 |
| x | 0.7 | 0.477016 | 1.467457 | 0.238542 | -0.81808 | 2.218076 |
he value of the standard error of the estimate=6.575
H0: β1 = 0
Ha: β1 ≠ 0
he value of the test statistic. T=1.467
p-value =0.2385
H0: β1 = 0
Ha: β1 ≠ 0
F=2.15
p=0.239
orchestra answered 1 year agoRelated Solutions
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