- definition of orthogonal
- difference between Y vector and X theta hat is 0?
- invert the matrix if full rank for solution

- X is a design matrix, first column is 1
- theta is params

- difference Y and Y hat (estimate)

- true signal + noise and prediction + residual

- The average of the fitted values is equal to average of the observed responses

- orthogonal to the residuals?

**Coefficient of Determination**
- variance of the fitted values
- variance of observed responses
- "percent of variance explained by the model"

- Change in y per unit change in x_1
**given all other variables held constant**

**colinearity**: when a covariate can be predicted by a linear function of others

- our model can be expressed as intercept, weight of features, and error

- We ha ve to estimate the weights (slopes)

- how do we test theta_1 is 0?

- could bootstrap, could build a confidence interval (?)