chpt 14 formulas

Question 1

Simple linear regression

bi = Slope =

Answer 1

Sum(xi-xbar)(yi-ybar) / sum(xi-Xbar)^2

Question 2

Intercept bo=

Answer 2

y bar - b1xbar

Question 3

Estimate regression equation

Answer 3

y hat = bo+b1x

Question 4

Coefficient of determination - SSE

Answer 4

(yi-ytrainalge hat)squared

Question 5

Coefficient of Determination - SST

Answer 5

(yi-ybar) squared

Question 6

Coefficient of Determination

- ssr (sum of squares due to regression)

Answer 6

SSR = SST- SSe

Question 7

Coefficient of determination

Answer 7

r squared = SSR/SST

Question 8

Correlation Coefficient

Answer 8

rxy = square root of r squared

Question 9

Ho: BI=0

Answer 9

1. Compute MSE
2. Compute standard error
3. compute estimate sd of bi
4. test statistic
5. calculate MSR
   def =
6. Calculate F ratio

Question 10

for HO: BI= 0 what is the formula for MSE

Answer 10

MSE = S squared = SSE/n-2

Question 11

for HO: BI= 0 what is the formula for Standard error

Answer 11

s = square root of MSE

Question 12

for HO: BI= 0 what is the formula for standard deviation of bi

Answer 12

sbi = s/sqaure root (sum (xi-xbar)squared

Question 13

for HO: BI= 0 what is the formula for the test statistic

Answer 13

t = bi - Bi / sbi

Bi=0

Question 14

for HO: BI= 0 what is the formula for Mean square regression?

Answer 14

MSR = SSR / 1

df =

Question 15

for HO: BI= 0 what is the formula for F ratio

Answer 15

F = MSR/ MSE
Df numerator = df for MSR
df denominator = df for MSE

Question 16

Anova table for simple linear regression - source of variation

Answer 16

Regression
Error
Total

Question 17

Confidence interval estimate standard deviation of y triangle hat *

Answer 17

Sytriangke hat * = s * square root (1/n + (x*-xbar)^2 / (xi-X bar)^2

Question 18

Formula for a confidence interval

Answer 18

Y trangke hat= bo+b1x

Y triangle hat= t a/2 sytrangke hat

Question 19

Prediction interval

Estimated sd of an indiviudal value of y when x =4

Answer 19

Spread = s* saiare root of

1+ 1/n+ (x*-xbar)^2 /(xi-x bar)^2

Question 20

Prediction interval

Answer 20

Y triangle hat * = ta/2 spread

Question 21

SSR (formula based) simple and multiple linear regression?

Answer 21

SSR = sum (y triangle hat i - Y bar)^2

Question 22

Multiple coefficient adjusted R2 for multiple regression

Answer 22

n = # of observations, p=# of I.V

R^2 a = 1 - (1-R^2) (n-1/n-p-1)

Question 23

Multiple regression MSE

Answer 23

MSE = SSE/ n-p-1

Question 24

Multiple regression MSR

Answer 24

MSR = SSR/p