Download Math 2345 EXAM # 3 Formula Sheet

Math 2345 EXAM # 3 Formula Sheet
χ2 Test: eq11.9: The test stat: χ2 =
P P
i
j
(fij −eij )2
,
eij
where eij =
(Row i T otal)(Column j T otal)
T otal sample size
Simple Linear Regression:
eq12.3: Estimated Simple
PRegression Equation: ŷ = b0 + b1 x
(xi − x)(yi − y)
P
eq12.6: The Slope b1 =
(xi − x)2
eq12.7: The Y-intercept: b0 = y − b1 x
P
eq12.8: Sum of squares Due to Error: P
SSE = (yi − ŷi )2
eq12.9: Total sum of squares: SST = (yi − ȳ)2
P
eq12.10: Sum of Squares Due to Regression: SSR = (ŷi − ȳ)2
eq12.11: Relationship Among SST,SSR,and SSE: SST = SSR + SSE
eq12.12: Coefficient of determination: r2 = SSR
SST
eq 12.15: Mean Square Error: s2 = M SE = SSE
n−2
q
eq12.16: Standard error of the estimate: s = SSE
n−2
s
eq12.18: Estimated Standard Deviation of b1 : sb1 = pP
(xi − x)2
b1
eq12.19: t Test Statistic tcal =
with (n − 2) degrees of freedom
Sb1
SSR
eq12.20: Mean Square Regression: M SR =
#indvar
M SR
eq12.21: F Test Statistic: F = M
SE
s
eq12.24: 100(1 − α)% CI for E(y ∗ ): ŷ ∗ ± tα/2 sŷ∗
where (eq12.23:) sŷ∗ = s
1
(x∗ − x̄)2
+P
n
(xi − x̄)2
Multiple Linear Regression:
eq13.3: Estimated multiple regression equation: ŷ = b0 + b1 X1 + b2 X2 + ... + bp Xp
SSR
SST
n−1
eq13.9: Adjusted Multiple Coefficient of Determination: Ra2 = 1 − (1 − R2 )
n−p−1
bi
eq13.15: t test Statistic: tcal =
with (n-p-1) degrees of freedom.
sbi
eq13.8: Multiple Coefficient of Determination: R2 =
Control Charts: Xbar :and R Chart
σ
eq15.1: Standard Error of the Mean: σx̄ = √
n
x̄ Chart for standard deviation known:
eq15.2: U CL = µ + 3σx̄
eq 15.3: LCL = µ − 3σx̄
x̄1 + x̄2 + · · · + x̄k
eq15.4: Overall Sample Mean: x̄ =
k
R1 + R2 + · · · + Rk
eq15.5: Average Range: R =
k
eq15.8: Control limits For an x̄ Chart for standard deviation unknown: x̄ ± A2 R̄
Control limits for an R chart:
eq15.14: U CL = RD4
eq15.15: LCL = RD3
Control Chart: p Chart
r
eq15.16: Standard Error of the Proportion: σp̄ =
Control Limits for a p Chart:
eq15.17: U CL = p + 3σp̄
eq15.18: LCL = p − 3σp̄
p(1 − p)
n