POWERPOINT 5

Question 1

picks the line that minimizes the sum of the squares of the residuals

Answer 1

least squares

Question 2

Y'i = b0+b1Xi
b0 = intercept
b1 = slope

Answer 2

linear prediction

Question 3

rxy * sy/sx
rxy = corr(x, y) is the sample correlation
sx and sy are the sample standard deviation of X and Y

Answer 3

b1

Question 4

Ybar - biXbar

Xbar and Ybar are the sample mean of X and Y

Answer 4

b0

Question 5

measure of centrality
n
Ybar = 1/n

Answer 5

sample mean

Question 6

measure of spread
n
sy^2= 1/n-1

Answer 6

sample variance

Question 7

sy = sqrt(sy^2)

Answer 7

sample standard deviation

Question 8

measures the direction and strength of the linear relationship between Y and X
n
Cov(Y, X) =

Answer 8

sample covariance

Question 9

sx+y^2 =sx^2 +sy^2 −Cov(X,Y)

Answer 9

relate sample variance and covariance as follows

Question 10

standardized covariance; scale invariance and the units of measurement don’t matter; only measures linear relationships
It is always true that −1 ≤ corr(X , Y ) ≤ 1
This gives the direction (- or +) and strength (0 → 1) of the linear relationship between X and Y
Corr(X, Y) = cov(X, Y)/sxsy

Answer 10

correlation

Question 11

In Summary: Y = Yˆ + e where:
Yˆ is “made from X”; corr(X,Yˆ) = 1
e is unrelated to X; corr(X,e) = 0

Answer 11

fitted values and residuals

Question 12

n



Answer 12

total sum of squares (SST)

Question 13

n



Answer 13

regression SS (SSR)

Question 14

n



Answer 14

error SS (SSE)

Question 15

SSR + SSE

Answer 15

SST

Question 16

measures goodness of fit; 0<1; gives the proportion of the variation in Y that can be explained by the variation in X; the closer to 1, the better the fit
R2 = SSR/SST = 1 − SSE/SST

Answer 16

coefficient of determination (R^2)

Question 17

correlation
R^2
SST, SSR, and SSE

Answer 17

evaluate how well the least square line can explain the data