17. Regression

Question 1

DIFFS BETWEEN corr/coeff

Answer 1

Regression is ASYMMETRIC - predicting one variable from one another

Cor. is symmetric

Regression uses relationship to predict Y from X

Question 2

X/Y in regression

Answer 2

X = explanatory

Y = response

Question 3

alpha and beta

Answer 3

alpha = y intercept

beta = slope

estimates = a and b!

Question 4

Y hat

Answer 4

value of Y predicted by value of X

Question 5

Residuals

Answer 5

Yi - Yi(hat)

Question 6

How do you decide which line is the BEST fit?

Answer 6

Least squares regression line!!!

Find a line that minimizes the sum of squares of residuals

Question 7

SSresiduals

Answer 7

sum from i = 1 to n of [Yi - Yi(hat)]^2

Question 8

What difference in variation is worrying?

Answer 8

more than a 10 fold difference in variance

Question 9

why shouldn’t you fit a polynomial w/ too many terms?

Answer 9

wouldn’t predict new data points!!

sample size at least 7 times number of terms!

Question 10

Confidence bands

Answer 10

telling us uncertainty for predicting an average value of y for a given value of x

Question 11

which is broader: prediction of where a line is or prediction of an individual?

Answer 11

individual - more uncertainty

Question 12

Prediction interval

Answer 12

uncertainty in estimating an individual value

Question 13

3 methods of fitting non linear relationships

Answer 13

1. transformations on data (ex log of both sides)
2. Quadratic regression
3. Splines

Question 14

Assumptions of Linear Regression + how to see on residual plot

Answer 14

1. random sample - cant see :(
2. Y normally distrib for all values of X - centered around line, tapers off
3. Y approx equal variance for all values of X - dots extend to similar points around the line

Question 15

problem with overfitting data

Answer 15

very poor predictive power for any new data points!!!!!