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

科目：研究所、轉學考(插大)◆統計學 | 年份：110年 | 選擇題數：0 | 申論題數：20

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 (20)

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

b. Calculate the geometric mean of y.(4 分)

c. Calculate the harmonic mean of y.(2分)

d. Calculate the standard deviation of y.(4 分)

e. Calculate the standard error of y.(3 分)

f. Calculate the median ofy.(3 分)

g. Calculate the 95% confidence interval of y.(5分)

a.Write down the solution for β_k in matrix notation.(5分)

b. Write down the solution forβ_r as a set of normal equation. (5分)

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)

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)

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)

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

b. What is a non-parametric hypothesis test for unpaired two-sample data? (2 分)

c. What is a non-parametric hypothesis test for paired two-sample data? (2 分)

d. What is a non-parametric hypothesis test for testing Normality assumption? (2 分)

e. The following is an ANOVA table, please fill in the blank (17 分)

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

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

c. What is the sampling distribution of an estimated mean? Please state the theorem and the distribution. (5 分) (10分)