simple linear regresion

Question 1

dependent variable - y

Answer 1

the variable we are seeking to explain

Question 2

independent variable - x

Answer 2

the explenatory variable -

Question 3

linear ligretion

Answer 3

assumes a linear relationship between the DV and IV

Question 4

variation of y

Answer 4

SSE = suma(yi-yśr)^2

to test how x explain y is we take SST = suma(yi-yh)^2
yh - odległość od lini regresji

if SSE = SST there is no diffrence
if SSE>SST x can be more described by y with the line

yi = b0+b1*xi +e

b0 = intercept
b1 = slope coeficient = cov(x,y)/variance(x)
both known as regression coeficient

Question 5

least squares method

Answer 5

residuals = distance from the reg line

best fit line = minimizes the sum of the squares deviations between the observed values of y and the predicted value of y

Question 6

intercept (interpretation)

Answer 6

yśr=b0 if xi=o

bi = the change in y for a one unit change in x

Question 7

linearity

Answer 7

the relationship between x and y is linear in the parameters. b0 and b1 cant be multiplied or divided by any regression parameter

Question 8

homoskedacticity

Answer 8

variance of (error) is the same for all observations if there is more than one it is a violation

Question 9

independence

Answer 9

pair of x and y should be independent. we should not be able to predict

Question 10

normality

Answer 10

error is normally distributed

Question 11

analysis of variance

Answer 11

1. SST=SSE+SSR
2. sum(yi-yśr)^2 = sum(yi-yh)^2+sum(yh-yśr)^2
3. total sum of squares = sum of squared errors(unexlained) = regression sum of squares (explained)

Question 12

coefficient of determination

Answer 12

measure of fit (not stat test) (R^2)

R^2 = SSR/SST = expl var/total var

how much variation of the independent value is being explained by the variation of the dependent value

Question 13

F-test of coeficient

Answer 13

f = MSR/MSE = var1/var2

F = SSR/k/SSE/n-(k+1)

k=slope coefficient
k+1 = regression coefficient

Question 14

Standard error of the estimate

Answer 14

SEE = sum(yi-yh)^2/(n-2))^1/2 = MSE^1/2

the lower the see the more accurate the regression

standard dev of the error term

Question 15

hypothesis test of b1

Answer 15

t = (bh-b1)/Sbh

Sbh = standard error of b1 (mianownik to SEE/pierw(suma(xi-xSr)^2

h0 = b1=0
h1 = b1=/0
bh = we should have

Question 16

hypothesis test of b0

Answer 16

we do it when b0 have a meaning (mostly it does not have)

t=(bh-b0)/Sbh

Question 17

log-lin model

Answer 17

ln(yi) = b0 +b1*xi

x is mostly time

Question 18

lin-log model

Answer 18

y=b0+b1*ln(x)

when y and x are significant different scale

Question 19

residual

Answer 19

error = yi=yh