Question

1.

A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in millimeters of mercury, for a sample of 6 adults. The following table presents the results.

Systolic	Diastolic
134	87
108	69
115	83
105	66
113	77
157	103

Part 1 of 2 

Compute the least-squares regression line for predicting diastolic pressure (v) from systolic pressure (x). Round the slope and y-intercept values to at least four decimal places. 

The regression equation is y = _______ 

Part 2 of 2 

Construct a 99% confidence interval for the slope. Round the answers to at least four decimal places. 

The 99% confidence interval is _______ < β1 < _______ 

2.

Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 6 pairs, with height measured in inches, simulated from the distribution specified by Pearson.

Father's height	Son's height
69.0	69.1
73.6	74.9
66.7	68.8
70.7	71.0
72.3	71.9
73.6	76.5

Part 1 of 2 

Compute the least squares regression line for predicting son's height() from father's height (x). Round the slope and y intercept values to at least four decimal places. 

The regression equation is y = _______ 

Part 2 of 2 

Construct a 95% confidence interval for the slope. Round the answers to at least four decimal places. 

The 95% confidence interval is  _______ < β1 < _______ 

Answer 1

1)

SSE =Syy-(Sxy)2/Sxx=

73.970

	s2 =SSE/(n-2)=	18.4925
std error σ              =	=se =√s2=	4.3003

std error of slope =se(β1) =s/√Sxx=

0.0965

for 99 % CI value of t=		4.604	(from excel:tinv(0.01,4)
margin of error E=t*std error =		0.4445
lower bound=b1+E=		0.2042
Upper bound=b1+E=		1.0932

99% Confidence interval =0.2042 <ß1 <1.0932

2)

from given data":

95 % Confidence interval =0.3879 <ß1 < 1.6748