112年 - [無官方正解]112 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#147624

科目：研究所、轉學考(插大)◆統計學 | 年份：112年 | 選擇題數：4 | 申論題數：21

試卷資訊

所屬科目：研究所、轉學考(插大)◆統計學

選擇題 (4)

1. Under which of the following conditions would you suggest that a double exponential smoothing model should be used instead of a single exponential smoothing model?

(A) When there are two main time-series variables involved in the forecast application
(B) When the data exhibit only random variation
(C) When the time-series data exhibit a trend
(D) When the data set is extremely uneven
2. In a simple exponential smoothing model, which of the following statements is true?

(A) The forecast values are determined by computing a moving average of the previous 4 data periods if we are working with quarterly data.
(B) The larger the smoothing constant, the more smoothing that takes place in the model.
(C) If the data contain a lot of random or irregular ups and downs, then a larger smoothing constant should be used in an attempt to model these fluctuations.
(D) More smoothing of the data will take place if a smoothing constant value close to zero is used.
3. Which of the following forecasting methods allows the decision maker to weigh the past time series differently to make the model more sensitive to more recent data?

(A) Exponential smoothing
(B) Linear trend regression model
(C) Moving average model
(D) De-seasonalizing the time series
4. A company has developed a linear trend regression model based on 16 quarters of data. The independent variable is the measure of time (t = 1 thru 16 where quarter 1 is winter quarter, 2 is spring, etc.). The company has also developed seasonal indexes for each quarter as follows:

| Winter | Spring | Summer | Fall |
| --- | --- | --- | --- |
| 1.20 | 1.00 | 0.70 | 1.10 |

The linear trend forecast equation is: $$\hat{y} = 120 + 56t$$.

Given this information, what is the seasonally adjusted forecast for period 19?

(A) 1,064
(B) 1,184
(C) 828.80
(D) 986.7

申論題 (21)

2. Research in Smoking Behaviours (30%)

*When the questions ask you to explain in 'plain language', it means your descriptions should 'let everyone who never studies statistics understand what you say'.

We were interested in understanding smokers' behaviours, so we conducted a survey, collecting data via a questionnaire with variables such as gender, age, number of cigarettes smoked per week, number of friends who smoke etc. The number of samples is 81. The followings are the given calculations:

- average number of cigarettes smoked per week: 78.70
-standard deviation of the number of cigarettes smoked per week: 68.21
- correlation coefficient for age and number of cigarettes smoked per week: 0.29

Based on the above information, please:

(1) Calculate the z-score for someone who smokes 100 cigarettes per week. Round both values to 2 decimals.
(2) Explain what the z-score means in plain language.
(3) Based on the correlation coefficient for age and the number of cigarettes smoked per week, please explain the relationship between these two variables in plain language.
We took two variables (number of cigarettes smoked per week and number of friends who smoke) to further examine their relationship, and came up with the equation to the trendline as the scatterplot below (y = 33.681x + 1.3326).

Based on the above information, please answer the following questions:

(4) Based on what you see in this scatterplot, determine which is the independent variable and which is the dependent variable, and explain the purpose of this regression analysis.
(5) Explain in plain language what the slope and the intercept mean respectively in this example.
(6) The R square value is 0.7264, please explain what it means in plain language.
(7) Based on the regression equation given, how many cigarettes would you expect someone to smoke in an average week if they have 4 friends who smoke? Show your calculations and round to a whole number.
(8) Can you also make a prediction for someone with 15 friends that smoke?
(9) Based on the results of the regression analysis, what could be the health implications to people who smoke?
3. You can find a Consumer Price Index (CPI) table of a fictional country 'Ostania' below, and answer the following two questions:(8%)

| Year | 2018 | 2019 | 2020 | 2021 | 2022 |
| --- | --- | --- | --- | --- | --- |
| CPI | 101.3 | 102.1 | 108.5 | 114.2 | 120.4 |

(1) Compared to 2020, how much more expensive are consumer goods and services in 2022 in Ostania? Calculate your answer in percentages and round to 2 decimals.
(2) Mr Loid Forger has been living in Ostania since 2020 and has earned €4250 net per month in 2020. In 2022 his salary was €4650 net per month. Has Mr Forger's salary, when adjusted for inflation, increased or decreased in 2022 compare to 2020? By what percentage? Show your calculations! (round to 2 decimals).
4. A metaverse company analyzes the sales situation in 111 years, and determines the relationship between the payment method and the price category of consumers to purchase metaverse goods, and obtains the following joint probability table.

| Item | cash | credit card | debit card |
| --- | --- | --- | --- |
| Below 10,000 yuan | 0.09 | 0.03 | 0.04 |
| 10,000--100,000 yuan | 0.05 | 0.21 | 0.18 |
| More than 100,000 yuan | 0.03 | 0.23 | 0.14 |

Please answer: (15 %)

(1) What is the proportion of consumer payments made by using debit cards?
(2) What is the probability that consumers will spend more than 100,000 yuan when they use a credit card to pay for a transaction?
(3) What is the proportion of purchases paid by consumers using credit or debit cards for financial transactions?
5. Assuming that the operating income of the head office and branches of the international business is in line with the binary normal distribution, the operating income of the international business head office in 111 year is subject to the normal distribution of the mean value is 170 and the standard deviation is 10. The operating income of the branch is subject to the normal distribution of mean value is 170 and the variance is 10. The correlation coefficient between these two is 0.6. Today, considering a group of international businesses with a total operating income of 175.

Please answer: (10 %)

(1) What is the average operating income of its branches?
(2) What is the proportion of operating income exceeding 175?
6. An international business uses a simple linear regression model to estimate the relationship between the number of advertisements X and the sales amount Y. According to the monthly data of the business from January to October, 111, the average value of the 10 sales is 130, while the variation is 1748. As for the average number of 10 advertisements, it is 14. Additionally, the covariance between the sales amount Y and the number of advertisements X is 316. Also, the regression equation estimated using the classical least squares method (OLS) is: Y = 60 + 5X.

Please answer: (25 %)

(1) If the sales amount in March is 88, and the number of advertisements in this month is 8. Please estimate the fitted value for the sales amount on March, 111.
(2) Continuing from the previous question, please estimate the residual value of the sales amount in March.
(3) Estimate the coefficient of determination \((\mathbb{R}^2)\).
(4) Please estimate the correlation coefficient (CORR) between the sales amount Y and the number of advertisements X.
(5) In the case that the significant level alpha \((\alpha)\) is equal to 0.05, please use the T test approach to test the hypothesis that the number of advertisements X affects the sales amount Y. That is, please check whether the slope value of the regression linear relationship is zero or not.