14.   The accompanying data on x = current density (mA/cm2) and y = rate of deposition (mm/min) ap- peared in the article Plating of 60/40 Tin/Lead Sol- der for Head Termination Metallurgy (Plating and Surface Finishing, Jan. 1997: 38—40). Do you agree with the claim by the article s author that a linear relationship was obtained from the tin—lead rate of deposition as a function of current density ? Ex- plain your reasoning.

 

along with their midparent heights in inches:

 

 

 

Midparent    66.0  65.5  71.5  68.0  70.0  65.5 67.0

 

Daughter     64.0  63.0  69.0  69.0  69.0  65.0  63.0

 

Midparent    70.5  69.5  64.5 67.5

 

Daughter     68.5  69.0  64.0  67.0

 

 

 

a.   Make a scatter plot of daughter s height against the midparent height and comment on the strength of the relationship.

 

b.   Is the daughter s height completely and uniquely determined by the midparent height? Explain.

 

c.    Use the accompanying MINITAB output to ob- tain the equation of the least squares line for pre- dicting daughter height from midparent height, and then predict the height of a daughter whose midparent height is 70 inches. Would you feel comfortable using the least squares line to pre- dict daughter height when midparent height is 74 inches? Explain.

 

 

 

Predictor	Coef	SE Coef	T	P
Constant	1.65	13.36	0.12	0.904
midparent	0.9555	0.1971	4.85	0.001

 

S = 1.45061 R-Sq = 72.3% R-Sq(adj) = 69.2%

 

 

 

Analysis of Variance

 

 

 

 

Regression 1 49.471 49.471 23.51  0.001 Residual 9 18.938 2.104   Error         Total 10 68.409       Â

Source        DF       SS       MS       F       P

 

 

 

 

15.  

x 20 40 60 80 y .24 1.20 1.71 2.22   Â

Refer to the data given in Exercise 1 on tank tem- perature and ef ciency ratio.

a.   Determine the equation of the estimated regres- sion line.

 

b.   Calculate  a  point  estimate  for  true   average ef ciency ratio when tank temperature is 182.

 

c.    Calculate the values of the residuals from the least squares line for the four observations for which temperature is 182. Why do they not all have the same sign?

 

d.   What proportion of  the  observed  variation in ef ciency ratio can be attributed to the simple

 

 

 

 

d.   What are the values  of  SSE,  SST,  and  the coef cient of determination? How well does the midparent height account for the variation in daughter height?

 

e.    Notice that for most of the families, the midparent height exceeds the daughter height. Is this what is meant by regression to the mean? Explain.