Sampling & Survey # 9 – Regression Estimation

Today, we shall look at regression estimation. We will begin by looking at the usual & simple straight line regression model: $y = B_0 + B_1 x$ . Let $\hat{B_1}$ and $\hat{B_0}$ by the ordinary least squares (OLS) regression coefficients of the slope and intercept.
$\hat{B_1} = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^n (x_i - \bar{x})^2}$ = $\frac{s_{xy}}{s_x^2}$ = $\frac{r s_y}{s_x}$
$\hat{B_0} = \bar{y} - \hat{B_1} \bar{x}$

Precision is increase, that is $SE(\hat{\bar{y}}_{reg}) < SE(\bar{y})$

Different estimators for population total

We conclude here by observing that ratio or regression estimators give greater precision that $\hat{t_y}$ when $\sum_{i=1}^n e_i^2$ for the method is smaller than $\sum_{i=1}^n (y_i - \bar{y})^2$

Sampling & Survey #1 – Introduction
Sampling & Survey #2 – Simple Probability Samples
Sampling & Survey #3 – Simple Random Sampling
Sampling & Survey #4 – Qualities of estimator in SRS
Sampling & Survey #5 – Sampling weight, Confidence Interval and sample size in SRS
Sampling & Survey #6 – Systematic Sampling
Sampling & Survey #7 – Stratified Sampling
Sampling & Survey # 8 – Ratio Estimation
Sampling & Survey # 9 – Regression Estimation
Sampling & Survey #10 – Cluster Sampling
Sampling & Survey #11 – Two – Stage Cluster Sampling
Sampling & Survey #12 – Sampling with unequal probabilities (Part 1)
Sampling & Survey #13 – Sampling with unequal probabilities (Part 2)
Sampling & Survey #14 – Nonresponse

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

Sampling & Survey # 9 – Regression Estimation

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