115年 - 115 國立臺北大學_碩士班一般入學考試試題_國際企業研究所：統計學#147120

科目：研究所、轉學考(插大)◆統計學 | 年份：115年 | 選擇題數：0 | 申論題數：18

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (0)

申論題 (18)

1. Please explain the following terminologies:

(1) Type I error (in hypothesis testing)
(2) Spurious correlation
(3) R squared \((\mathbb{R}^2)\) (in regression analysis)
2. Please give an example for the following terminologies respectively:

(1) Type I error
(2) Spurious correlation
3. For Type I error, please name the most important reason why it may occur.
4. For R squared, please interpret the figures of \(\mathbb{R}^2\)
Session 2 (15%)

1. Suppose we get these seasonal indexes for a restaurant based on 3 years' sales figures in the follow table.

| Season | Seasonal Index |
| --- | --- |
| Spring | ? |
| Summer | 1.420 |
| Autumn | 0.920 |
| Winter | 0.820 |

(1) Please interpret the Summer and Winter indexes.
(2) Find seasonal index for Spring.
(3) Based on these indexes, what kind of advice you would give to the restaurant owner in terms of operational management?
Session 3 (50%)

1. The economics score (X) and statistics score (Y) of a school's international business graduate school enrollment are shown in the table below: Now it has been obtained: (10 %)

| X | 30 | 68 | 24 | 31 | 49 |
| --- | --- | --- | --- | --- | --- |
| Y | 63 | 80 | 58 | 64 | 71 |

Now ΣX=202, ΣY=336, ΣX²=9,462, ΣY²=22,870, ΣXY=14,185 have been obtained.

(1) Please calculate the correlation coefficient between economics scores and statistics scores.
(2) Now I want to use economics scores to estimate statistical scores. Please make a regression line based on the above data.
2. The patrol police at the Shulin Station on the second highway want to know if the average speed of the truck is too high. Today, 81 trucks were randomly selected to measure their speed, and found that the average speed was 105 kilometers per hour and the standard deviation was 6 kilometers per hour, and it was assumed that the population obeyed the normal distribution. Please answer the following question: Does the average speed of a truck exceed 100 kilometers per hour under a significant level of 0.05? (Please write the null hypothesis and the opposing hypothesis, then calculate the statistic value and P value, respectively, and explain your statistical results). (15 %)
3. A school secretariat wants to understand the influencing factors of the job satisfaction score (Y) of its contracted employees. Consider four explanatory variables (X1, X2, X3, X4):

X1: Years of service (years).

X2: Salary level (thousand yuan).

X3: Whether you have a bachelor degree, X3=1 means you have a bachelor degree; X3=0 means no bachelor degree. (BA)

X4: Master's degree or above, X4=1 means master's degree or above; X4=0 means no master's degree or above. (MA)

Now, the data of 30 contracted employees are obtained, and the dependent variable Y is regression analysis for four independent variables (X1, X2, X3, X4), and the estimated regression model in the following table is obtained.

| | Estimated coefficients | Standard errors |
| --- | --- | --- |
| Intercept | 13.24 | 7.29 |
| X1 | 8.69 | 2.56 |
| X2 | 1.35 | 0.38 |
| X3 | 4.92 | 2.10 |
| X4 | 5.89 | 4.10 |

Note: SST = 989.7; s = 4.8. SST represents total sum of square, and s represents the estimate deviation of the standard error of regression. Please answer the following five questions. (25 %)

(1) Please explain the significance of the estimated regression coefficients of X3 and X4, respectively.
(2) Please use a significance level of 0.05 to test the significance of the regression coefficients of X3 and X4, respectively.
(3) Please present the ANOVA table and then test whether the F-value of this regression model is significant.
(4) Please calculate the adjusted coefficient of determination of this regression model.
(5) Please calculate the mean squared error value of this model and explain its meaning.