chpt 14 formulas Flashcards
Simple linear regression
bi = Slope =
Sum(xi-xbar)(yi-ybar) / sum(xi-Xbar)^2
Intercept bo=
y bar - b1xbar
Estimate regression equation
y hat = bo+b1x
Coefficient of determination - SSE
(yi-ytrainalge hat)squared
Coefficient of Determination - SST
(yi-ybar) squared
Coefficient of Determination
- ssr (sum of squares due to regression)
SSR = SST- SSe
Coefficient of determination
r squared = SSR/SST
Correlation Coefficient
rxy = square root of r squared
Ho: BI=0
- Compute MSE
- Compute standard error
- compute estimate sd of bi
- test statistic
- calculate MSR
def = - Calculate F ratio
for HO: BI= 0 what is the formula for MSE
MSE = S squared = SSE/n-2
for HO: BI= 0 what is the formula for Standard error
s = square root of MSE
for HO: BI= 0 what is the formula for standard deviation of bi
sbi = s/sqaure root (sum (xi-xbar)squared
for HO: BI= 0 what is the formula for the test statistic
t = bi - Bi / sbi
Bi=0
for HO: BI= 0 what is the formula for Mean square regression?
MSR = SSR / 1
df =
for HO: BI= 0 what is the formula for F ratio
F = MSR/ MSE
Df numerator = df for MSR
df denominator = df for MSE
Anova table for simple linear regression - source of variation
Regression
Error
Total
Confidence interval estimate standard deviation of y triangle hat *
Sytriangke hat * = s * square root (1/n + (x*-xbar)^2 / (xi-X bar)^2
Formula for a confidence interval
Y trangke hat= bo+b1x
Y triangle hat= t a/2 sytrangke hat
Prediction interval
Estimated sd of an indiviudal value of y when x =4
Spread = s* saiare root of
1+ 1/n+ (x*-xbar)^2 /(xi-x bar)^2
Prediction interval
Y triangle hat * = ta/2 spread
SSR (formula based) simple and multiple linear regression?
SSR = sum (y triangle hat i - Y bar)^2
Multiple coefficient adjusted R2 for multiple regression
n = # of observations, p=# of I.V
R^2 a = 1 - (1-R^2) (n-1/n-p-1)
Multiple regression MSE
MSE = SSE/ n-p-1
Multiple regression MSR
MSR = SSR/p
