Question

You may need to use the appropriate technology to answer this question. Consider the data. xi 3 12 6 20 14 yi 55 40 55 10 15 (a) Compute the mean square error using equation s2 = MSE = SSE n − 2 . (Round your answer to two decimal places.) (b) Compute the standard error of the estimate using equation s = MSE = SSE n − 2 . (Round your answer to three decimal places.) (c) Compute the estimated standard deviation of b1 using equation sb1 = s Σ(xi − x)2 . (Round your answer to three decimal places.) (d) Use the t test to test the following hypotheses (α = 0.05): 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 = State your conclusion. Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant. Reject H0. We cannot conclude that the relationship between x and y is significant. Do not reject H0. We conclude that the relationship between x and y is significant. Correct: Your answer is correct. (e) Use the F test to test the hypotheses in part (d) at a 0.05 level of significance. Present the results in the analysis of variance table format. Set up the ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to three decimal places.) Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Regression Error Total 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. Do not reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We cannot conclude that the relationship between x and y is significant. Reject H0. We conclude that the relationship between x and y is significant. Do not reject H0. We conclude that the relationship between x and y is significant.

Answer #1

Following table shows the calculations:

X | Y | X^2 | Y^2 | XY | |

3 | 55 | 9 | 3025 | 165 | |

12 | 40 | 144 | 1600 | 480 | |

6 | 55 | 36 | 3025 | 330 | |

20 | 10 | 400 | 100 | 200 | |

14 | 15 | 196 | 225 | 210 | |

Total | 55 | 175 | 785 | 7975 | 1385 |

Sample size: n=5

Now,

(a)

Let us find SSE first :

The MSE is

(b)

The standard error of the estimate using equation is

(c)

The standard error of slope is

(d)

Slope of the regression equation is

The test statistics is

Degree of freedom: df=n-2=3

The p-value is: 0.0193

Since p-value is less than 0.05 so we reject the null hypothesis.

Reject H0. We conclude that the relationship between x and y is significant.

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