3. Aug 24th

Question 1

Can the null hypothesis be true?

Answer 1

Yes, in a controlled manipulative study.

Question 2

What are multiple types of regression tests an example of?

Answer 2

The general linear model

- The most important topic of this entire class

Question 3

What is the simplest form of the general linear model?

Answer 3

Simple linear regression

- Continuous x, continuous y

Question 4

What are the two purposes of regression?

Answer 4

1. Fit a line to data
2. Test if the slope of that line is significant
   - – If p-value < 0.05

Question 5

What are the three possible causes of a large p-value?

Answer 5

If the p-value > 0.05, we don’t know if:
A) Sample size is too small
B) Effect size is too small
C) Too much noise

Question 6

The traditional equation for a line

Answer 6

y = mx + b

b is the y intercept
m is the slope (change in y value/change in x value)

Question 7

The stats equation for a line

Answer 7

General
Y = Beta-0 + Beta-1(X)
B0 is a constant
B1 is regression coefficient

Specific
y-hat = Beta-0 + Beta-1(X)
y-hat = predicted value of dependent variable

Question 8

What two elements make up the relationship between every x and y (i.e. the line)?

Answer 8

Our equation PLUS Epsilon

E = error (normally distributed)

Question 9

What two requirements must be met to be a “best fit line”?

Answer 9

1. Average error = 0
   - – (The distance from each point to the line added up)/n = 0
2. The sum of squared error is minimized
   - – Squaring to get rid of negatives
   - – Complicated models are done iteratively

Question 10

What is the more technical name for “total variance in y”?

Answer 10

Total Sum of Squares

Total Sums of Squares (SST): summed square of distance from data to null hypothesis line (0 slope)
Represents ALL the information we have
SST = SSR + SSE

Sigma(n top, i=1 bottom) (Yi - y-bar)^2
Yi - any individual Y (observed dependent variable)
Y-bar- average/mean y

Question 11

What 2 things does the total sum of squares partition variation into?

Answer 11

https://365datascience.com/sum-squares/

1. SSR- sum of squares due to regression
   — The variation in y due to variation in x
   Sigma(n top, i=1 bottom) (Yi-hat - y-bar)^2
   Yi-hat = Your predicted value of y
   Y-bar = average/mean of Ys AKA mean of the dependent variable
2. SSE- sum of squares due to error
   — Noise
   Sigma(n top, i=1 bottom) (ei^2)
   e = difference between the observed value and the predicted value

Question 12

What type of p-value will you get if sum of square error (SSE) is larger than sum of squares regression (SSR)?

Answer 12

A large p value (greater than 0.05)

Question 13

What type of p-value will you get if sum of squares regression (SSR) is greater than sum of squares error (SSE)?

Answer 13

A smaller p-value (smaller than 0.05)

Also means that movement in y is mostly due to x

Question 14

Important take aways of regression

Answer 14

1) Best fit lines mean
- –a) Average error = 0
- –b) Minimize sum of squares error (SSE)

2) P-values are calculated by partioning variation in y into
- – Sum of squares regression (SSR)
- – Sum of squares error (SSE)

Question 15

What does regression display?

Answer 15

Correlation

NOT causation

Question 16

What DO you have to do to determine causation?

Answer 16

A MANIPULATIVE experiment.

Observational studies will not prove causation.

This is the VERY reason that debates about global warming even exist.
— We don’t have 3 Earths to manipulate. We cannot do manipulative studies.

Question 17

How can you test to be absolutely sure your R data results are correct?

Answer 17

Make the data yourself.

Question 18

What does the professor not believe in?

Answer 18

“I don’t believe in randomness. Randomness is just other measurable things we haven’t measured.”

Question 19

How to load data to R

Answer 19

1) datum=read.csv(file.choose())

2) head(datum)

Question 20

How to plot in R

Answer 20

plot(Y~X,data=datum)

Question 21

How to run almost any regression in R

Answer 21

lm(same inside as plot)

Question 22

What does he recommend you save your results as?

Answer 22

results

results=lm(Biomass~Rainfall, data=datum)
summary(results)

Question 23

What single function gives you most of the data you’re looking for in your results?

Answer 23

summary()

Question 24

What is R^2?

Answer 24

The proportion of variation in y explained by x

If:
R^2 = 1, all points are on the regression line. Perfect fit.
R^2 = 0, no slope, no points on the line

R^2 always goes up when you add x-values