4: Exploratory Data Analysis—Simple Regression

Question 1

regression lines

Answer 1

summarizes relationship b/w two variables ONLY WHEN one of the variables helps explain or predict the other

that is, describes relationship b/w explanatory variable and response variable

Question 2

y = b0 + b1x

Answer 2

b1 = slope 
b0 = intercept, value of y when x=0

Question 3

least squares regression line

Answer 3

least squares regression line of y on x is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible

Question 4

equation of the least-squares regression line

Answer 4

y-hat = b0 + b1X

slope = b1 = r * (Sy/Sx)

intercept = b0 = y-bar = b1*x-bar

Question 5

r^2

Answer 5

the fraction of the variation in the value of y that is explained by the least-squares regression of y on x

variance of predicted values y-hat / variance of observed values

Question 6

residual plot

Answer 6

scatterplot of the regression residuals against the explanatory variable. residual plots help us assess the fit of a regression line

Question 7

points that are outliers in the ____ direction of a scatterplot are often influential for the least-squares regression line

Answer 7

x

Question 8

causation

Answer 8

Correlation is NOT causation
even a very strong association b/w 2 variables is not by itself good evidence that there is a cause-and-effect link b/w the two variables.

Question 9

reverse causation

Answer 9

does x cause y or y cause x?

Question 10

common response

Answer 10

z causes both x and y

Question 11

confounding

Answer 11

z is correlation with x and with y, so cannot separate the effect of x on y alone.