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Results tagged with regression
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user 189634
Techniques for analyzing the relationship between one (or more) "dependent" variables and "independent" variables.
1
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1
answer
349
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Conditional Variance of Linear Regression Coefficients $Cov(\hat{\beta}_0,\hat{\beta}_1|W^*)$
I'm trying to determine $Cov(\hat{\beta}_0,\hat{\beta}_1|W^*)$ for
$$
Z=\beta_0+\beta_1W+\xi
$$
where $\xi|W \sim N(0, \sigma^2)$ where $\hat{\beta}_0=\bar{W}-\hat{\beta}_1\bar{Z}$ and $\hat{\beta_1}= …
- 367
1
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1
answer
71
views
Value of $\sum_{j=1} (y_{j} - \bar{y})$ and proving properties of hat value
The i-th fitted value $\hat{Z}_i$ is written as a linear amalgam of response values $\hat{Z}_i=\sum_{j=1}h_{ij}Z_j$ where $h_{ij}=\frac{1}{n}+\frac{(y_i-\bar{y})(y_j-\bar{y})}{S_{yy}}$ and $S_{yy}=\su …
- 367
1
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1
answer
5k
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Linear regression $y_i=\beta_0 + \beta_1x_i + \epsilon_i$ covariance between $\bar{y}$ and $...
I am currently reading through slides from Georgia Tech on linear regression and came across a section that has confused me. …
- 367