Anonymous

# 統計問題(需懂英文)----有關迴歸

【題組】In an effort to explain to customers why their electricity bills have been so high lately, and how, specifically, they could save money by reducing the thermostat settings on both space heaters and water heaters, an electric utility company has collected total kilowatt consumption figures for last year’s winter months, as well as thermostat settings on space and water heaters, for 100 homes.

Regression Statistics

Multiple R 0.8415

R Square 0.7081

Standard Error 213.7

Observations 100

ANOVA

df SS MS F Significance F

Regression 2 10744454 5372227117.640.0000

Residual 97 4429664 45667

Total 99 15174118

Coefficients Standard Error t Stat P-value

Intercept 576.8 514.0 1.120.2646

Space 90.61 6.48 13.990.0000

Water 9.66 2.41 4.000.0001

( )1. Which of the following statement is correct? (A)The regression equation is yˆ = 576.8 + 90.61Space + 9.66 Water (B)The standard error of estimate is = 213.7 (C)70.81% of the variation in sales is explained by the model (D)The model fits reasonably well (E)All of the above.

( )2.Test the validity of the model. (A)Since F = 117.64, there is no evidence to conclude that the model is valid (B)Since p-value = 0, there is no evidence to conclude that the model is valid (C)Atα= 5%, there is enough evidence to conclude that the model is valid (D)Since R2 = .7081, there is no evidence to conclude that the model is valid

( )3.About the coefficients of Space, which of the following statement is correct? (A)Atα= 1%, “Space” should be retained in the model (B)Atα= 5%, “Space” should not be retained in the model (C)Atα= 10%, “Space” should not be retained in the model (D)Atα= 5%, “Space” should not be retained in the model

Rating

( ) 1. Which of the following statement is correct? (A)The regression equation is yˆ = 576.8 + 90.61Space + 9.66 Water (B)The standard error of estimate is = 213.7 (C)70.81% of the variation in sales is explained by the model (D)The model fits reasonably well (E)All of the above.

（A）迴歸方程式為 yˆ = 576.8 + 90.61Space + 9.66 Water，對！

（B）迴歸估計的標準誤為 213.7 ，對！

（C）銷售變異的70.81% 可以被模型解釋，對！

（D）模型的擬合程度合理，對！

（E）以上皆是，對！

( ) 2.Test the validity of the model. (A)Since F = 117.64, there is no evidence to conclude that the model is valid (B)Since p-value = 0, there is no evidence to conclude that the model is valid (C)Atα= 5%, there is enough evidence to conclude that the model is valid (D)Since R2 = .7081, there is no evidence to conclude that the model is valid

（A）因為 F = 117.64，沒有證據推論模型有效，錯！

（B）因為 p-value = 0，沒有證據推論模型有效，錯！

（C）在顯著水準α= 5% 下，有足夠證據推論模型有效，對！（p-value = 0 < α= 5%）

（D）因為 R2 = .7081，沒有證據推論模型有效，錯！

( ) 3.About the coefficients of Space, which of the following statement is correct? (A)Atα= 1%, “Space” should be retained in the model (B)Atα= 5%, “Space” should not be retained in the model (C)Atα= 10%, “Space” should not be retained in the model (D)Atα= 5%, “Space” should not be retained in the model

（A）在α= 1%下，Space應該留在模型中，對！（p-value = 0 < α= 5%，非常顯著）

（B）在α= 5%下，Space不應該留在模型中，錯！

（C）在α= 10%下，Space不應該留在模型中，錯！

（D）在α= 5%下，Space不應該留在模型中，錯！