Question

A research chemist wants to understand how several predictors are associated with the wrinkle resistance of cotton cloth. The chemist examines 32 pieces of cotton cellulose produced at different settings of curing time, curing temperature, formaldehyde concentration, and catalyst ratio. The durable press rating, a measure of wrinkle resistance, is recorded for each piece of cotton. She runs a regression that yields the following: 2. Rating -0.7560 0.1545*Conc +0.2171 *Ratio+0.01081 Temp0.0946 Time a. Is the regression significant if SST 65.7049 and SSE 17.7953? Use a 0.025. b. What are R2 and Radj? Are there insignificant terms in the model? c. She computes se(Bconc)0.0633. Is Bconc a significant term in the model using α 0.025?

Answer 1

a)

SSR=SST-SSE

MS=SS/df

f-stat = MSr/MSe

Anova table
variation	SS	df	MS	F-stat	p-value
regression	47.9096	4	11.98	18.1728	0.0000
error,	17.7953	27	0.66
total	65.7049	31

since p-value<alpha=0.025,regression model is significant

b) R² = SSR/SST = 0.7292

no. of predictors ,k =4

n=32

R² adj = 1 - [(1-R²)(n-1)/(n-k-1))=   0.6890

c)

Ho:   ß = 0  
Ha:   ß ╪ 0  
      
n =   32  
alpha,α =    0.025  
estimated slope=   0.1545  
std error =    0.0633  
      
t-test statistic =    t = estimated slope / std error =   2.4408
      
Df =    n - 2 =   30
p-value =    0.0208  

since p-value <α=0.025, rehect Ho

so, it is a significant term