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研究所、轉學考(插大)◆統計學題庫 下載題庫

110 年 - 110 國立臺灣大學_碩士班招生考試_森林環境暨資源研究所丙組:統計學(D)#102063 

選擇:0題,非選:20題 我要補題 回報試卷錯誤
【非選題】
1.
1. Given a sample data, y= (8, 6, 5, 10, 9}, please answer the following questions (25 分):

【題組】 a. Calculate the arithmetic mean of y.(4 分)


【非選題】
2.【題組】b. Calculate the geometric mean of y.(4 分)

【非選題】
3.【題組】c. Calculate the harmonic mean of y.(2分)

【非選題】
4.【題組】d. Calculate the standard deviation of y.(4 分)

【非選題】
5.【題組】e. Calculate the standard error of y.(3 分)

【非選題】
6.【題組】f. Calculate the median ofy.(3 分)

【非選題】
7.【題組】g. Calculate the 95% confidence interval of y.(5分)

【非選題】
8.

2. Y=β01•X12•X23•X3 +εis a multiple linear regression model with Y being the response variable, βk the k-th regression coefficient, andXk the k-th predictor. Please answer the following questions (25 分):
61652c9b6c687.jpg


【題組】a.Write down the solution for βk in matrix notation.(5分)


【非選題】
9.【題組】b. Write down the solution forβr as a set of normal equation. (5分)

【非選題】
10.【題組】c. When the above multiple linear regression model is fitted to a dataset, what type of test will you use to test for model overall goodness of fit? Piease name the test. the test statistics, and the probability density function associated with the test. (5 分)

【非選題】
11.【題組】d. When the above multiple linear regression model is fitted to a dataset, what type of test will you use to test whether an estimated coefficient is significant different than zero? Please name the test, the test statistics, and the probability density function associated with test. (5 分)

【非選題】
12.【題組】e. When the above multiple linear regression model is fitted to a dataset, one of the outputs is multiple-R2. What does multiple-R2 explain? What is the equation for calculating multiple-R2?(5分)

【非選題】
13.
3. Please answer the following questions above hypothesis testing (25 分):

【題組】 a. What is a non-parametric hypothesis test for one-sample data? (2 分)


【非選題】
14.【題組】b. What is a non-parametric hypothesis test for unpaired two-sample data? (2 分)

【非選題】
15.【題組】c. What is a non-parametric hypothesis test for paired two-sample data? (2 分)

【非選題】
16.【題組】d. What is a non-parametric hypothesis test for testing Normality assumption? (2 分)

【非選題】
17.【題組】e. The following is an ANOVA table, please fill in the blank (17 分)

【非選題】
18.
4. Please answer the following questions (25 分):

【題組】

a. Prove sample variance can be written in two ways, i.e., prove  61652ccbac6bb.jpg



【非選題】
19.【題組】

b. Prove that 61652cf95986b.jpg is a biased estimator for sample variance (10分)



【非選題】
20.【題組】c. What is the sampling distribution of an estimated mean? Please state the theorem and the distribution. (5 分) (10分)

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110 年 - 110 國立臺灣大學_碩士班招生考試_森林環境暨資源研究所丙組:統計學(D)#102063-阿摩線上測驗

110 年 - 110 國立臺灣大學_碩士班招生考試_森林環境暨資源研究所丙組:統計學(D)#102063