Problem 1 (20 pts) Please identify the roles of following items(notations) into

Question

Problem 1 (20 pts) Please identify the roles of following items(notations) into 4 categories, which are giveh values calculated values, parameters, or random variables. Please fill into the following table with the corresponding notations.P ISample mean of a given sample, y c 2 Independent variable, X G Dependent variable, Yv f v Coefficient in the regression model, The least squared estimator, bi 2v b v' Error term, ev 1 Residual, e v The first observation in a particular sample, (xi, yi) aV q v' ( v' t!The predicted value of y for the first observation, The error of the first observation, ! The residual of the first observation,'eN cu Sampling error based on a particular sample, IBi - bil The predicted value of x for a given value of xp based on the least squared estimator, p kv Confidence interval estimate, C.I.E. CVAN , f estimat c ko Prediction interval estimetaPLE UN t

Explanation / Answer

A) 1. sample mean is calculated vaue as we calculate it with the given sample values (c)

2. random variable

3. random variable because independent and dependent variables are random variables denoted by capital letters

4.parameter regression coefficient is a slope and regression equations are used to estimate the parameters

5. the least squared estimate is random variable

6. error is an amount by which an observation differ by its mean value as it is randomly choosen so it is a random variable it is independent variable.

7. residual is observable estimate of error so it is dependent variable hence it is random variable

8. given values from the sample we will take the first observation . second etc

9. random variable

10. random variable

11. calculated value because predicted values can be calculated by the values only

12. .parameter

13 random variable

14. calculated value by using mean ,proportion etc usind table values and sd

15 calculated value

16 random variable because it represents the results of a calculated values by using random sample

17 . calculated value as we calculate the test values using the values

18.random variable as the sample is notspecified we have to take a random sample

19. cv ,we have to calculate it first correlation then squaring it we will get coef of determination

20 gv these are calculated by using the given sample size

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