Stat 131a

What is a DGP?

It stands for the data generating process. It is the underlying process used to gather the data points. it is unobserved.

What does it mean to be 95% confident?

If we repeat the sample many times with similar parameters, approximately 95% of the calculated confidence intervals will capture the true population parameter.

point estimate formula

lower + upper / 2

moe formula

upper - lower / 2

how to get Estimated SE

get the moe (easy to get with confidence intervals)
se = moe/ (z(alpha)/2)

65 95 99 rule

65 - 1 sd

95 - 1.96 (best 2 )

99 - 3

formula for SD of sample mean

s / sqrt(n)

s stands for…

As sample size n increases what decreases? what else does this cause?

standard error. this will be squeezing confidence interval too.

What is a p-value?

the probability of obtaining a sample statistic at least as extreme as the observed value, assuming the null hypothesis is true

SE formula for confidence intervals.

SE formula for Hypothesis test

pH0 ——- the hypothesized null value

R code for calculating a 2-sided p-value.

2 * pnorm(phat, mean = , sd = sqrt( fill in ))

• fill in the sd as the formula ph0 that is given

in a confidence interval, if H0 falls in confidence interval you :____

in a confidence interval, if H0 does not fall inside the confidence interval you : ____

inside interval : fail to reject the null

outside interval : reject the null

what is statistical power? whats the easiest way to increase power?

the probability of rejecting H0 when H0 is false.

to increase power, increase sample size.

What do r and and sd fall on?

the point of averages (xhat, yhat)

What is the formula for the SD line? what does SD measure?

ssd = sy/sx
it measures spread of the data points.

What is the regression slope formula?

r * sy/sx (sd technically)

what does r = on a perfect correlation? on no correlation?

r = 1 on perf

r = 0 on none

what does the sd and r line look like?

sd is right across from bottom left to top right symmetrical.

r line is different.

what does it mean for correlation to be scale invariant

no matter if you convert r from inches to feet, R² will be unchanged

What is regression to the mean?

extreme X values (both high or low) lead to predicted Y values that are closer to the mean Y.

How do you get Residual?

actual Y - predicted Y

What is RSS and how do you get it?

1. get the ( actual - predicted ) of every value

2. square every values.

3. add all the squared values to each other.

RSS = sum of all values residuals squared.

What is essential to reconstruct a data generating equation?

• you need the error.

What is bootstrapping to for standard errors?

1. resample n times with replacement

2. refit the regression model to get a synthetic slope

3. repeat it 10,000 times

4. take the sd of the synthetic slopes.

in a model with no predictors, what is the best guess?

best guess is the sample mean Yhat.
TSS = sum of all y -yhat all squared.

What is R²?

it is the percentage of variation in Y explained by the linear model.

for an intercept only baseline model: R² = 0

What does it mean for R² to be 0? what about 1?

It means that if it is 0, the model is not a good predictor other then the average. 1 is that it predicts better.

What does RMSE measure?

it measures average prediction error in the original units of Y

When you add predictors (covariates) what happens to R² and RMSE

R² will increase or stay the same

RMSE will decrease or stay the same

Interpret an intercept.

The predicted average outcome when all numeric variables = 0 and all categorical variables are at their reference level.

Interpret a covariate/variable

The estimated average difference in outcome for a group compared to the reference level holding all other variables constant.

Marginal Effects in Quadratic Models

do the derivative of the quadratic model for changes in y with respect to x

lm (y ~ 1, data = ..)

1. single intercept model

   1. aka the baseline model

lm( y ~ 1 + x , data = …)

1. single intercept, single slope

   1. simple linear model

2. 
   

lm( y ~ 1 + x1 + x2, data = …)

1. multiple intercepts, single slope model

   1. parallel lines

lm ( y ~ 1 + x1 * x2, data = …)

1. multiple intercepts, multiple slopes model

   1. interaction model

Do we need TSS or or RSS to be smaller?

RSS < TSS

because RSS is squaring every actual - predicted.

What’s the formula for R²

1 - TSS/RSS

What’s the formula for MSE

RSS / n