Question

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12 15 The estimated regression equation is ? = 0.7 + 2.7x. Compute the mean square error using the following equation (to 3 decimals). Compute the standard error of the estimate using the following equation (to 3 decimals). Compute the estimated standard deviation b1 using the following equation (to 3 decimals). Use the t test to test the following hypotheses (? = .05): H0: B1 = 0 Ha: B1 /= 0. Compute the value of the t test statistic (to 2 decimals).

Answer #1

The statistical software output for this problem is:

**Simple linear regression results:**

Dependent Variable: yi

Independent Variable: xi

yi = 0.7 + 2.7 xi

Sample size: 5

R (correlation coefficient) = 0.93831486

R-sq = 0.88043478

Estimate of error standard deviation: 1.8165902

**Parameter estimates:**

Parameter |
Estimate |
Std. Err. |
Alternative |
DF |
T-Stat |
P-value |
---|---|---|---|---|---|---|

Intercept | 0.7 | 1.9052559 | ? 0 | 3 | 0.36740472 | 0.7377 |

Slope | 2.7 | 0.57445626 | ? 0 | 3 | 4.7000967 | 0.0182 |

**Analysis of variance table for regression
model:**

Source |
DF |
SS |
MS |
F-stat |
P-value |
---|---|---|---|---|---|

Model | 1 | 72.9 | 72.9 | 22.090909 | 0.0182 |

Error | 3 | 9.9 | 3.3 | ||

Total | 4 | 82.8 |

Hence,

MSE = 3.3

Standard error = 1.817

Estimated standard deviation = 0.574

t test statistic = 4.70

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1
2
3
4
5
yi
53
58
47
21
11
Use the estimated regression equation is y-hat = 78.01 -
3.08x
A.) Compute the mean square error using
equation.
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[ ] (to 2 decimals)
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6
9
13
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18
9
26
23
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9
13
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